[livro] estatística espacial com aplicações em epidemiologia, economia e sociologia

136
Frqwhýgr

Upload: cicero-souza

Post on 21-Apr-2015

490 views

Category:

Documents


62 download

TRANSCRIPT

Page 1: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

��������

4 Lqwurgxêær 4

414 Dqäolvh hvsdfldo h qær0hvsdfldo gh gdgrv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6

415 Wlsrorjld grv gdgrv hvsdfldlv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8

41514 Gdgrv gh Surfhvvrv Srqwxdlv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8

41515 Gdgrv gh vxshuiðflh dohdwöuld 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 44

41516 Gdgrv gh äuhd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 46

41517 Gdgrv gh lqwhudêær hvsdfldo 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 47

416 D suäwlfd gd dqäolvh gh gdgrv hvsdfldlv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 48

417 Vlvwhpdv Jhrjuä�frv gh Lqirupdêær h Hvwdwðvwlfd Hvsdfldo 1 1 1 1 1 4;

5 Dqäolvh gh Gdgrv gh Äuhd 54

514 Lqwurgxêær 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 54

515 Pdwul} gh shvrv hvsdfldlv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 54

516 Pdsdv frpr judirv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 55

517 Dxwrfruuhodêær hvsdfldo 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 59

518 Dxwrfruuhodêær hvsdfldo frp wd{dv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5<

6 Pdshdphqwr gh grhqêdv 64

614 Lqwurgxêær 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 64

615 Prghor Foävvlfr gh Ulvfrv Uhodwlyrv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 66

616 Pdsdv gh suredelolgdghv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 73

617 Hvwlpdêær ed|hvldqd hpsðulfd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 76

61714 Ed|hv Hpsðulfr h r Sdudgr{r gh Vwhlq 1 1 1 1 1 1 1 1 1 1 1 1 76

l

Page 2: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

FRQWHÝGR 4

61715 Wd{dv h ulvfrv uhodwlyrv frpr yduläyhlv dohdwöuldv 1 1 1 1 1 1 77

61716 Hvwlpdgru ed|hvldqr olqhdu öwlpr 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7:

61717 Xp h{hpsor vlpsohv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7;

61718 Hvwlpdgruhv gh Ed|hv olqhduhv öwlprv 1 1 1 1 1 1 1 1 1 1 1 1 7<

61719 Hvwlpdgru öwlpr olqhdu ed|hvldqr hpsðulfr 1 1 1 1 1 1 1 1 1 83

6171: Hvwlpdgru lqwhludphqwh ed|hvldqr 1 1 1 1 1 1 1 1 1 1 1 1 1 1 84

7 Pdsdv ed|hvldqrv gh grhqêdv 86

714 R uhyhuhqgr Ed|hv qr �p gr vìfxor 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 86

715 Prghor klhuäutxlfr ed|hvldqr sdud pdsdv gh grhqêdv 1 1 1 1 1 1 1 88

71514 Ghfrpsrvlêær gr ulvfr uhodwlyr 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 89

71515 Glvwulexlêær grv Klshusduåphwurv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8;

71516 Glvwulexlêær d Srvwhulrul 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8;

716 Sulrulv Hvsdfldophqwh Hvwuxwxudgdv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8<

71614 Fdpsrv dohdwöulrv gh Pdunry frpr glvwulexlêøhv d sulrul 1 8<

71615 Whruhpd gh Kdpphuvoh| h Fol�rug 1 1 1 1 1 1 1 1 1 1 1 1 1 1 93

71616 Sulrulv hvsdfldlv sdud gdgrv frp glvwulexlêær qrupdo 1 1 1 1 9:

717 Lpsohphqwdêær 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :4

718 H{hpsor 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :5

719 H{whqvøhv= prghorv gh hvsdêr h whpsr 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;3

8 Whvwhv gh Frqjorphudgrv ;:

814 Whvwhv jhqìulfrv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <7

81414 Pìwrgr JDP gh Rshqvkdz 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <7

81415 Pìwrgr gh Ehvdj h Qhzho 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <:

81416 Dgdswdêær gr pìwrgr gh Fx}lfn h Hgzdugv 1 1 1 1 1 1 1 1 1 433

81417 Pìwrgr gh Yduuhgxud gh Nxoogrui 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 433

815 Whvwhv irfdgrv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 437

81514 Dgdswdêær grv pìwrgrv dqwhulruhv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 439

81515 Whvwh gh hvfruh 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 43:

81516 Whvwh gh Vwrqh +4<;;, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 43<

816 Frqfoxvøhv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 445

Page 3: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

5 FRQWHÝGR

Devwudfw

Hvwdvwðvwlfd hvsdfldo ì xp udpr gd hvwdwðvwlfd txh hvwxgd pìwrgrv flhqwð�frv

sdud d frohwd/ ghvfulêær/ ylvxdol}dêær h dqäolvh gh gdgrv txh srvvxhp frrughqdgdv

jhrjuä�fdv1 Vxd pdufd glvqwlqwlyd ì r xvr h{soðflwr rx lpsoðflwr ghvwdv frru0

ghqdgdv jhrjuä�fdv qd prghodjhp1 R hqruph ghvhqyroylphqwr frpsxwdflrqdo

uhfhqwh ì r uhvsrqväyho gluhwr shor ruhvflphqwr gd äuhd hvsdfldo hp hvwdwðvwlfd1

Hp sduwlfxodu/ r ghvhqyroylphqwr gh judqghv vlvwhpdv jhrjuä�frv gh lqirupdfær

d xp fxvwr uhgx}lgr whp srvvlelolwdgr h hvwlpxodgr d fuldfær gh judqghv edvhv gh

gdgrv jhruhihuhqfldgdv1

Hvwh fxuvr hvwä yrowdgr sdud xp vxe0frqmxqwr gh wìfqlfdv gh hvwdwðvwlfd hvsdfldo

txh wudedokd frp pdsdv gh xpd uhjlær sduwlflrqdgd hp äuhdv h frp xp rx pdlv

dwulexwrv dvvrfldgrv frp fdgd äuhd1 Qr fdsðwxor lqwurgxwöulr ydprv prvwudu rv

rxwurv wlsrv gh gdgrv hvsdfldlv h{lvwhqwhv h glvfxwlu r wlsr gh dqäolvh txh ì uhdol}dgd

hp fdgd xp ghohv1

Hvwh fxuvr irl hvfulwr whqgr hp phqwh xp doxqr gh �p gh judgxdêær hp hv0

wdwðvwlfd rx lqðflr gh phvwudgr1 R suì0uhtxlvlwr sdud vxd ohlwxud ì d idploldulgdgh

frp lqihuíqfld hvwdwðvwlfd h/ hp sduwlfxodu/ lqihuíqfld ed|hvldqd xvdqgr PFPF1

Hqwuhwdqwr/ vxd íqidvh ì dsolfdgd surfxudqgr vhpsuh dsuhvhqwdu d glvfxvvær grv

frqfhlwrv ýwhlv sdud d suäwlfd gd dqäolvh gh gdgrv gh äuhd hvsdfldlv1

Lqihol}phqwh/ qær irl srvvðyho freulu wrgr r hvshfwur gh dsolfdføhv h gh whruld h

pìwrgrv hqyroylgrv qhvwh wlsr gh gdgrv pdv r txh hvwä h{srvwr dtxl vhuyh frpr

xpd lqwurgxfær d dojxqv grv sulqflsdlv sureohpdv/ frqfhlwrv h prghorv hqyroylgrv

qd dqäolvh gh gdgrv gh äuhd1 D sulqflsdo äuhd gh dsolfdfær frehuwd qhvwh wh{wr

ì d gd vdýgh sýeolfd txh srvvxl xpd judqgh lqwhudfær frp hvwdwðvwlfd1 Doìp

glvwr/ wudwd0vh gd äuhd hp txh r dxwru dfxpxorx pdlv h{shulíqfld frp rv vhxv

sureohpdv h wìfqlfdv hvshfð�frv1 Dshvdu glvwr/ r fuhvflphqwr uäslgr ghvwd äuhd

frp d lqwurgxfær gh qrydv lgìldv h pìwrgrv ì pxlwr judqgh h krxyh xp prphqwr

hp txh xpd ghflvær whyh gh vhu wrpdgd= d gh id}hu gr olyur xpd reud dwxdol}dgd

pdv freulqgr vxshu�fldophqwh pxlwdv wìfqlfdv rx uhgx}lu r hvfrsr h dxphqwdu

d glvfxvvær gh fdgd wöslfr1 Hx rswhl shod vhjxqgd h hvshur txh whqkd vlgr hp

ehqhiðflr gd pdlruld grv ohlwruhv1 Qr hqwdqwr/ r vhqwlphqwr �qdo ì dpeðjxr txdqgr/

Page 4: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

FRQWHÝGR 6

dr whuplqdu yäuldv sduwhv/ uhfher r qryr qýphur gxsor +4:24;, gd Vwdwlvwlfv lq

Phglflqh/ yroxph 4< gh 5333/ 733 säjlqdv wrwdophqwh ghyrwdgdv d dqäolvh hvsdfldo

gh gdgrv hp vdýgh1

R ohlwru txh vh lqwhuhvvdu hp dsurixqgdu qhvwh dvvxqwr ghyh frphfdu frp xp

olyur wh{wr h phx idyrulwr ì r olyur gh Edloh| h Jdwuhoo +4<<8, txh dlqgd ì phokru

lqwurgxfær vreuh r dvvxqwr= dsolfdgr/ fkhlr gh h{hpsorv prwlydgruhv/ frp xp

vriwzduh dfrpsdqkdqgr r olyur h frp jduqgh foduh}d qdv h{solfdføhv1 Rxwur olyur

wh{wr ì r gh Fuhvvlh +4<<9, txh/ qr hqwdqwr/ sduhfh vhu pdlv xp frqmxqwr gh qrwdv

gh dxod qær pxlwr ehp rujdql}dgdv1 Hqwuhwdqwr/ hoh ì pxlwr frpsohwr h vhuyh

frpr olyur gh uhihuíqfld1 Pdlv dqwljrv/ pdv ljxdophqwh lpsrwdqwhv/ vær Fol� h Rug

+4<;4, h Ulsoh| +4<<4,1 H{lvwhp yäulrv rxwur olyurv pdlv yrowdgrv sdud shvtxlvd

txh hvwær vhqgr hglwdgrv uhfhqwhphqwh hp hvwdwðvwlfd hvsdfldo h txh vær gh lqwhuhvvh

jhudo1 R sulqflsdo ì Odzvrq hw do1 +4<<<,/ xp h{fhohqwh olyur wrwdophqwh yrowdgr

sdud dsolfdføhv qd äuhd gd vdýgh1 Hp sruwxjxív/ r ohlwru srgh hqfrqwudu xp öwlpr

wh{wr rq0olqh qdv säjlqdv gr LQSH= kwws=22zzz1gsl1lqsh1eu2jloehuwr2olyur1

Hx txhur djudghfhu drv rujdql}dgruhv gd Hvfrod gh Prghorv gh Uhjuhvvær/ h

hp sduwlfxodu dr surihvvru Iudqvflvfr Orx}dgd0Qhwr/ shor frqylwh sdud hqvlqdu xp

plqlfxuvr/ frp xp wh{wr gh dfrpsdqkdphqwr/ gxudqwh hvwh hyhqwr1 Djudghfr

lphqvdphqwh ã sdflíqfld h erd yrqwdgh dwì d hqwuhjd �qdo gr pdqxvfulwr1 Txhur

wdpeìp djudghfhu ã Hydqjholqd [dylhu/ gr LEJH/ shod dmxgd frp rv pdsdv gh

Vær Sdxor +sdud yduldu grv pdsdv gh Ehor Krul}rqwh h gh Plqdv Jhudlv,1

Ghl{hl sdud r �qdo xp djudghflphqwr pxlwr hvshfldo h fdulqkrvr sdud d Gud1

P÷qlfd V1 Prqwhlur0gh0Fdvwur txh dmxgrx0ph ohqgr rv ruljlqdlv/ surgx}lqgr rv

pdsdv ed|hvldqrv h id}hqgr yäuldv fuðwlfdv h phokruldv qr wh{wr1 Vh yrfí vhqwlu

txh dojxpd sdvvdjhp hvwä ehp hvfulwd/ dfuhglwh/ irl judfdv d hod1 Txdqwr drv huurv

gh uhylvær h rplvvøhv txh uhvwdp/ hohv vær wrgrv phxv +h qhp suhflvr shglu sdud

yrfí dfuhglwdu qlvwr/ qìB,1

Hvwh wh{wr irl hvfulwr gxudqwh dv iìuldv gh Gh}hpeur h gh Mdqhlur h/ sru lvwr/

srgh0vh rxylu yäuldv yh}hv gxudqwh vxd ohlwxud r vxvslur sdflhqwh gh phxv �okrv/

txh vh yludp sulydgrv gr sdl pdlv gr txh vhuld ud}räyho1

Page 5: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7 FRQWHÝGR

Page 6: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

Fdsðwxor 4

��������

Hvwdvwðvwlfd hvsdfldo ì xp udpr gd hvwdwðvwlfd txh hvwxgd pìwrgrv flhqwð�frv sdud

d frohwd/ ghvfulêær/ ylvxdol}dêær h dqäolvh gh gdgrv txh srvvdp vhu prghodgrv fr0

pr surfhvvrv hvwrfävwlfrv/ rqgh r hvsdêr ðqglfh ì xp frqmxqwr gh glphqvær pdlru

txh xp1 Xvxdophqwh/ rv surfhvvrv hvwrfävwlfrv vær frohêøhv gh yduläyhlv dohdwöuldv

i[w> w 5 W j rqgh r hvsdêr gr ðqglfh w ì xp vxefrqmxqwr gd uhwd/ xvxdophqwh uhsuh0

vhqwdqgr r whpsr/ glvfuhwr rx frqwðqxr1 Vìulhv whpsrudlv h dqäolvh gh vreuhylyíqfld

vær dojxqv grv h{hpsorv gh surfhvvrv hvwrfävwlfrv pdlv frqkhflgrv qd olwhudwxud

hvwdwðvwlfd/ r sulphlur xvxdophqwh frp xp frqmxqwr gh ðqglfh W @i3>4>5> ===j h rvhjxqgr frp W @ ^3>4`1 Hp hvwdwðvwlfd hvsdfldo/ W vhuä xvxdophqwh xp vxefrq0

mxqwr gh U5/ pdlv ududphqwh gh U61 Hvwh frqmxqwr srghuä vhu glvfuhwr rx frqwðqxr/

�qlwr rx lq�qlwr1

R hqruph ghvhqyroylphqwr frpsxwdflrqdo uhfhqwh ì r uhvsrqväyho gluhwr shor

ruhvflphqwr gd äuhd hvsdfldo hp hvwdwðvwlfd1 Dv wìfqlfdv gh hvwdwðvwlfd hvsdfldo

wíp vhuylgr d xp hqruph ohtxh gh dsolfdêøhv1 Dqäolvh gh h{shulphqwrv djuðfrodv/

gh lpdjhqv gh vdwìolwh rx gljlwdlv/ gh sdguøhv gh pruelgdgh/ dsolfdêøhv jhriðvlfdv/

hp djurqrpld h hp plqhudêær/ hvwxgrv hfroöjlfrv gh frpxqlgdghv gh sodqwdv

h hvwxgrv gh qhxurdqdwrpld/ wrgdv vær äuhdv txh vh ehqh�fldudp pxlwr ghvvdv

wìfqlfdv h irudp wdpeìp äuhdv edvwdqwh dwlydv qr ghvhqyroylphqwr gh pìwrgrv gh

hvwdwðvwlfd hvsdfldo1

4

Page 7: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

5 FDSÐWXOR 41 LQWURGXÊÆR

Hslghplrorjld h vdýgh sýeolfd hp jhudo vær äuhdv txh srvvxhp judqgh lqwhuhvvh

hp wìfqlfdv gh dqäolvh gh gdgrv jhruhihuhqfldgrv1 Uh hwlqgr hvwh lqwhuhvvh gd

glvflsolqd h d h{shulíqfld gr dxwru/ hvwh olyur ydl xvdu h{whqvdphqwh h{hpsorv

gh hslghplrorjld sdud prwlydu rx loxvwudu dv wìfqlfdv1 Hp sduwlfxodu/ pdsdv gh

dwulexwrv hslghplroöjlfrv/ wdlv frpr wd{dv gh lqflgíqfld rx suhydoíqfld gh grhqêdv

rx fdudfwhuðvwlfdv gh srsxodêøhv/ frqvwlwxhp xp srghurvr lqvwuxphqwr sdud r

hqwhqglphqwr gd hslghplrorjld gh xp sureohpd gh vdýgh sýeolfd1 D pdqhlud

xvxdo gh prvwudu d glvwulexlêær hvsdfldo gh xpd grhqfd ì sru phlr gh pdsdv1

Pdv pdsdv sru vl phvprv qær vær ýwhlv d phqrv txh qöv srvvdprv ghvfuhyí0orv/

frpsduä0orv h lqwhusuhwä0orv1 Hvwdwðvwlfd ghvfulwlyd rx lqihuhqfldo ì ýwlo rx/ dojxpdv

yh}hv/ hvvhqfldo sdud wruqdu h{soðflwr r txh hvwä dshqdv lpsoðflwr qhvwhv pdsdv rx

sdud dqdolvä0orv1

Hvwdwðvwlfd qdr ì d ýqlfd irupd gh h{wudlu lqirupdêær vreuh sdguøhv dohdwöulrv

pdv hod srvvxl wuív fdudfwhuðvwlfdv pdufdqwhv=

41 Hvwdwðvwlfd dglflrqd suhflvær d xpd ghvfulêær txdolwdwlyd1

51 Hvwdwðvwlfd idflolwd d frpsdudêær hqwuh glihuhqwhv srsxodêøhv qr hvsdfr rx qr

whpsr xvdqgr fulwìulrv remhwlyrv +sruwdqwr/ uhsurgxwðyhlv, h txdqwlwdwlyrv1

61 Hvwdwðvwlfd srgh fkdpdu d dwhqêær sdud fdudfwhuðvwlfdv txh qdr hudp shufhs0

wðyhlv sru phlr gh xpd lqvshêær txdolwdwlyd1

Hvwhv wuív dvshfwrv hvwær suhvhqwhv hp hvwdwðvwlfd hvsdfldo qdv wuív irupdv foäv0

vlfdv hp txh d hvwdwðvwlfd ì xvdgd= sdud vlvwhpdwl}du d irupd gh frohwdu gdgrv

hvsdfldlv/ sdud h{sorudu h ylvxdol}du hvwhv gdgrv hp pdsdv rx phglgdv uhvxpr/ h

sdud h{wudlu frqfoxvøhv vreuh r phfdqlvpr jhudgru grv gdgrv edvhdgr hp prgh0

orv suredeloðvwlfrv1 Dojxpdv ghvwdv irupdv foävvlfdv hvwduær pdlv suhvhqwhv qhvwh

olyur pdv qhvwh fdsðwxor ydprv frphqwdu xp srxfr vreuh fdgd xpd ghodv1 Qd

suö{lpd vhêær/ ydprv glvwlqjxlu xpd dqäolvh hvwdwðvwlfd hvsdfldo gh xpd dqäolvh

qær0hvsdfldo1 D vhjxlu/ ydprv dsuhvhqwdu d wlsrorjld foävvlfd grv gdgrv hvsdfl0

dlv glylglgd hp txdwur fdwhjruldv= gdgrv gh surfhvvrv srqwxdlv/ gdgrv gh äuhd

+qd txdo hvwh olyur hvwä frqfhqwudgr,/ gdgrv gh vxshuiðflhv dohdwöuldv h gdgrv gh

lqwhudêær hvsdfldo1 D vhjxlu/ ydprv glvfxwlu dojxqv dvshfwrv suäwlfrv gd dqäolvh

Page 8: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

4141 DQÄOLVH HVSDFLDO H QÆR0HVSDFLDO GH GDGRV 6

hvsdfldo/ dsuhvhqwdu dojxqv frphqwäulrv vreuh d lqwhuidfh hqwuh hvwdwðvwlfd hvsdfldo

h vlvwhpdv jhrjuä�frv gh lqirupdêær h whfhu dojxqv frphqwäulrv vreuh d vlwxdêær

eudvlohlud qr txh vh uhihuh ã dqäolvh gh gdgrv gh äuhd yrowdgd sdud dvshfwrv gd

uhdolgdgh vrfldo rx hfrq÷plfd1

414 Dqäolvh hvsdfldo h qær0hvsdfldo gh gdgrv

Rv gdgrv xwlol}dgrv hp hvwdwðvwlfd hvsdfldo srvvxhp xp ðqglfh txh id} uhihuíq0

fld d xpd äuhd jhrjuä�fd/ jhudophqwh uhsuhvhqwdgd hp xp pdsd elglphqvlrqdo1

Hqwuhwdqwr/ sudwlfdphqwh wrgrv rv gdgrv gh txdotxhu ihq÷phqr txh hvwhmd vhqgr

hvwxgdgr srvvxhp dojxp wlsr gh orfdol}dêær hvsdfldo1 Lvwr srgh vh gdu dr qðy0

ho gd jhrjud�d iðvlfd/ frpr hp gdgrv vrfldlv rx hfrq÷plfrv hp pxqlfðslrv qxp

pdsd fduwrjuä�fr rx gdgrv lqglylgxdlv qxp hvwxgr foðqlfr gh fdvr0frqwuroh rqgh

xp grv gdgrv ì d uhvlgíqfld gr lqglyðgxr1 Srgh vh gdu wdpeìp qxpd wrsrjud�d

pdlv devwudwd/ wdo frpr gdgrv gh vlqdsvhv gh qhxu÷qlrv orfdol}dgrv qr hvsdfr

wulglphqvlrqdo gr fhuìeur1 Ghvwh prgr/ sudwlfdphqwh wxgr txh srgh vhu dqdolvd0

gr hvwdwlvwlfdphqwh srvvxl uhihuíqfld hvsdfldo1 Hvwd d�updêær ì xpd wulyldolgdgh

vhphokdqwh d gl}hu txh wrgd lqirupdêær hvwdwðvwlfd srvvxl xpd uhihuíqfld whp0

srudo1 Reyldphqwh/ lvwr qær wruqd wrgd dqäolvh hvwdwðvwlfd xpd wìfqlfd gh vìulhv

whpsrudlv rx gh hvwdwðvwlfd hvsdfldo1

D fdudfwhuðvwlfd ixqgdphqwdo gh xpd wìfqlfd gh dqäolvh hvsdfldo ì txh d uhihu0

íqfld jhrjuä�fd ì xwlol}dgd h{solflwdphqwh qr prghor1 Dvvlp/ xpd dqäolvh gh

uhjuhvvær olqhdu vlpsohv xvdqgr frpr yduläyho ghshqghqwh dv wd{dv gh krplfðglr

pxqlflsdlv hp Plqdv Jhudlv hp 5333 h frpr yduläyho lqghshqghqwh r SLE shu

fdslwd pxqlflsdo hp 4<<; qær ì xpd dqäolvh hvsdfldo phvpr txh dv xqlgdghv gh

revhuydêær +rv pxqlfðslrv plqhlurv, whqkdp hylghqwhphqwh xpd orfdol}dêær hvsd0

fldo1 D txhvwær ì txh d uhihuíqfld hvsdfldo qær irl xwlol}dgd hp qhqkxp prphqwr

qr surfhvvr gh dqäolvh1 Mä xp pdsd grv uhvðgxrv ghvwd uhjuhvvær olqhdu ruglqäuld

srghuld vhu fkdpdgr gh xpd wìfqlfd h{sorudwöuld gh ylvxdold}dêær hvsdfldo1 Dvvlp/

r txh glvwlqjxh dv wìfqlfdv gh hvwdwðvwlfd hvsdfldo ì r xvr h{solfðwr gdv frrughqdgdv

hvsdfldlv grv gdgrv qr surfhvvr gh frohwd/ ghvfulêær rx dqäolvh grv gdgrv1

Page 9: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7 FDSÐWXOR 41 LQWURGXÊÆR

Qrvvr lqwhuhvvh qhvwh olyur uhvlgh qd vlwxdêær pxlwr frpxp hp txh dv xqlgdghv

gh dqäolvh vær hqwlgdghv frp orfdol}dêær jhrjuä�fd wdlv frpr pxqlfðslrv/ plfur

uhjløhv/ xqlgdghv gh sodqhmdphqwr/ edluurv/ hwf1 Qhvwdv vlwxdêøhv/ qær ì srvvðy0

ho vxsru txh rv ydoruhv gdv yduläyhlv revhuydgdv qd pdwul} gh gdgrv hqwuh gxdv

xqlgdghv txdlvtxhu vhmdp lqghshqghqwhv1 Gh idwr/ ì öeylr txh ghyhuhprv hvshudu/

hp jhudo/ fhuwd vlplodulgdgh rx fruuhodêær hqwuh xqlgdghv txh vhmdp yl}lqkdv qr

hvsdêr1 Gdgd d frqwlqxlgdgh gdv dwlylgdghv vöflr0hfrq÷plfdv qr hvsdêr h d du0

elwudulhgdgh grv olplwhv dgplqlvwudwlyrv/ srghprv hvshudu txh xqlgdghv suö{lpdv

whqgdp d vhu pdlv vlploduhv txh xqlgdghv glvwdqwhv1

Txdlv dv frqvhtÿíqfldv gd suhvhqêd gd hvwuxwxud hvsdfldo hqwuh dv xqlgdghv gh

dqäolvhB Sru xp odgr/ hod ydl uhsuhvhqwdu fhuwd uhgxqgåqfld gh lqirupdêær hqwuh

dv xqlgdghv/ uhgx}lqgr r wdpdqkr hihwlyr gd dprvwud xwlol}dgd qd dqäolvh1 Sdud

hqwhqghu hvwh dvshfwr/ lpdjlqh txh/ ghylgr ã vxd yl}lqkdqêd/ gxdv xqlgdghv vær

wær fruuhodflrqdgdv txh vær sudwlfdphqwh lgíqwlfdv1 Dvvlp/ xpd ghvvdv xqlgdghv

qær frqwulexl frp qhqkxpd lqirupdêær dglflrqdo vreuh r phfdqlvprv jhudgru gh

gdgrv doìp gr txh d rxwud mä frqwulexl1 Ì fodur txh fdvrv h{wuhprv frpr hvvh vær

udurv pdv hohv loxvwudp r sulqfðslr jhudo gh txh d dxwr0fruuhodêær hqwuh dv xqlgdghv

id} frp txh d lqirupdêær frqwulexðgd sru fdgd xqlgdgh/ dglflrqdophqwh ãv rxwudv

xqlgdghv/ qær vhmd ljxdo ã xqlgdgh1 Sruwdqwr/ hvvd ì xpd frqvhtÿíqfld qhjdwlyd

gd dxwr0fruuhodêær hvsdfldo sdud d dqäolvh idwruldo1

D rxwud frqvhtÿíqfld uhohydqwh gd dxwr0fruuhodêær ì srvlwlyd srlv hod shu0

plwh phokrudu dv hvwlpdwlydv gh sduåphwurv hvshfð�frv gh fdgd äuhd ghylgr ã

uhgxqgåqfld gh lqirupdêøhv qrv yl}lqkrv1 Lvwr rfruuh txdqgr dv yduläyhlv vöflr0

hfrq÷plfdv vær wd{dv/ dv txdlv srvvxhp xp hihlwr gh wdpdqkr dvvrfldgr= rv ydoruhv

gh xqlgdghv frp shtxhqdv srsxodêøhv gh ulvfr +ghqrplqdgruhv shtxhqrv, srvvxhp

ydulåqfld pxlwr pdlru txh dv xqlgdghv frp judqghv srsxodêøhv gh ulvfr1 Dr xvdu

d lqirupdêær gh txh rv yl}lqkrv whqghp d vhu vlploduhv/ srghprv hvwlpxodu rv

sduåphwurv hvwlpdgrv frp pxlwd yduldelolgdgh +ghylgr dv shtxhqdv srsxodêøhv,

d qær vhu wær glvfuhsdqwhv grv vhxv yl}lqkrv1 D whqgíqfld gh hvwlpxodu d vlplodul0

gdgh hqwuh rv sduåphwurv gh äuhdv yl}lqkdv ghshqghuä gr wdpdqkr gd srsxodêær

gd xqlgdgh1 Dtxhodv frp judqgh srsxodêær qær vhuær dihwdgdv hqtxdqwr dtxhodv

Page 10: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

4151 WLSRORJLD GRV GDGRV HVSDFLDLV 8

frp shtxhqdv srsxodêøhv +h hvwlpdwlydv xvxdlv lqvwäyhlv, srghp vhu hvwdelol}dgdv

h srghp vriuhu phqrv grv hihlwrv gr shtxhqr wdpdqkr gh vxd srsxodêær1

415 Wlsrorjld grv gdgrv hvsdfldlv

Rv glihuhqwhv wlsrv gh gdgrv hvsdfldlv vær wudglflrqdophqwh fodvvl�fdgrv gh dfrugr

frp xpd wlsrorjld gh txdwur fdwhjruldv1 Hvwd fdwhjrul}dêær gl} uhvshlwr ã qdwxuh}d

hvwrfävwlfd gd revhuydêær1 Dv fdwhjruldv vær dv vhjxlqwhv=

41 Gdgrv gh Surfhvvrv Srqwxdlv1

51 Gdgrv gh Vxshu�flhv Dohdwöuldv1

61 Gdgrv gh Äuhd1

71 Gdgrv gh Lqwhudêær Hvsdfldo1

Frpr r txh glvwlqjxh hvwdv fdwhjruldv ì r wlsr gh gdgr dohdwöulr/ ì qdwxudo

txh hp fdgd xp ghvwhv txdwur wlsrv h{lvwdp pìwrgrv hvwdwðvwlfrv glihuhqwhv sdud

ghvfuhyhu rx dqdolvdu rv gdgrv1 Hvwh olyur hvwä frqfhqwudgr dshqdv qxp grv wlsrv

dflpd/ gdgrv gh äuhd/ frp rfdvlrqdlv phqêøhv drv gdgrv gh surfhvvrv srqwxdlv1

Hqwuhwdqwr/ ydprv ghvfuhyhu euhyhphqwh rv txdwur wlsrv foävvlfrv gh gdgrv h r

frqwh{wr hp txh vxujhp1

41514 Gdgrv gh Surfhvvrv Srqwxdlv

Vær rv frqmxqwrv gh gdgrv hp txh r sulqflsdo lqwhuhvvh hvwä qr frqmxqwr gh fr0

rughqdgdv jhrjuä�fdv uhsuhvhqwdqgr dv orfdol}dêøhv h{dwdv gh hyhqwrv wdlv frpr

dv uhvlgíqfldv gh lqglyðgxrv grhqwhv rx rv orfdlv gh urxerv d pær dupdgd qxpd

flgdgh1 Qhvwh fdvr/ r gdgr dohdwöulr gh lqwhuhvvh ì d suösuld orfdol}dêær hvsdfldo gr

hyhqwr1 Lpdjlqh xpd irokd gh sdsho hp eudqfr hp txh dojxqv srqwrv/ rx hyhqwrv/

dsduhfhp dohdwruldphqwh1 Hvwh wlsr gh phfdqlvpr jhudgru gh gdgrv dohdwöulrv ì

r ihq÷phqr gh lqwhuhvvh dtxl1 Dvvlp/ r txh ì dohdwöulr qhvwh wlsr gh gdgrv ì d

suösuld orfdol}dêær gr hyhqwr qr pdsd1

H{hpsor= D Iljxud 414 prvwud xp pdsd gh Ehor Krul}rqwh frp dv orfdol}dêøhv

h{dwdv gdv uhvlgíqfldv gh xpd dprvwud dohdwöuld gh 866 lqglyðgxrv txh grdgr0

Page 11: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

9 FDSÐWXOR 41 LQWURGXÊÆR

udp vdqjxh qd Ixqgdêær Khprplqdv +khprfhqwur hvwdwdo gh uhihuíqfld hp Plqdv

Jhudlv,/ hp Ehor Krul}rqwh/ qr shuðrgr gh 4<<7 d 4<<9 +Prqwhlur0gh0Fdvwur hw do1/

5334,1 Hqwuh rxwudv txhvwøhv/ hud gh lqwhuhvvh qhvwh sureohpd vdehu vh rv grdgruhv

gh vdqjxh lqihfwdgrv shor yðuxv KWOY0L2LL hvwdydp glvwulexðgrv jhrjud�fdphqwh

gh irupd vhphokdqwh drv grdgruhv qær lqihfwdgrv rx vh/ shor frqwuäulr/ whqgldp d

whu xp rxwur hvsdokdphqwr hvsdfldo vxjhulqgr txh/ sdud hvwd vxesrsxodêær/ h{l0

vwluldp idwruhv klvwöulfrv/ wdoyh} gh dvvhqwdphqwr/ rx idwruhv vrfldlv txh �}hvvhp

frp txh lqglyðgxrv gh glihuhqwhv uhjløhv srvvxðvvhp glihuhqwhv fkdqfhv gh whuhp

lqihfêær shor yðuxv KWOY0L2LL1

H{hpsor= D Iljxud BBprvwud xpd ylvær sdufldo gh Ehor Krul}rqwh freulqgr pdlv

gh 83( gd äuhd gr pxqlfðslr frp vxdv äuhdv gh idyhod +uhjløhv hp flq}d, h äuhdv

yhughv +uhjløhv hp yhugh, ghpdufdgdv1 Fdgd srqwr uhsuhvhqwd d orfdol}dêær hvsd0

fldo gh xp fulph ylrohqwr +krplfðglr/ urxer/ urxer d pær dupdgd/ hvwxsur/ hwf1,

uhjlvwudgr shod Sroðfld Plolwdu gh Plqdv Jhudlv hp 4<<;1 Hqwuh rxwudv txhvwøhv gh

lqwhuhvvh/ h{lvwhp yäuldv shujxqwdv txh gl}hp uhvshlwr ã orfdol}dêær hvsdfldo ghvvhv

hyhqwrv1 Sru h{hpsor/ ghvhmd0vh vdehu vh d jhrjud�d grv fulphv frqwud d shvvrd

ì glihuhqwh gd jhrjud�d grv fulphv frqwud d sursulhgdgh1 Ì frpxp hqfrqwudu rv

fulphv frqwud d shvvrd orfdol}dgrv hp äuhdv pdlv sreuhv hqtxdqwr txh rv fulphv

frqwud d sursulhgdgh whqghp d hvwdu orfdol}dgrv hp äuhdv uhodwlydphqwh pdlv ulf0

dv1 Ì lpsruwdqwh txdqwl�fdu hvwd glvfuhsåqfld hqwuh hvwhv grlv wlsrv gh fulph sdud

frpsduä0od frp d rxwudv flgdghv rx dfrpsdqkdu vxd hyroxêær qr whpsr1

Dojxqv sureohpdv wðslfrv gh gdgrv hvsdfldlv vre d irupd gh surfhvvrv srqwxdlv

vær rv vhjxlqwhv= h{lvwh djorphudêær gh fdvrv rx hohv hvwær glvsrvwrv dr �dfdvr� B

Hvwdu suö{lpr d dojxpd �irqwh� +sru h{hpsor/ xp ulr rx xpd iäeulfd sroxlgrud,

dxphqwd r ulvfr gh xp lqglyðgxr wruqdu0vh xp fdvr gh dojxpd hqihuplgdgh +sru

h{hpsor/ xpd grhqfd frqwdjlrvd rx xpd grhqfd uhvsludwöuld,B Yhu/ sru h{hpsor/

Eljjhul hw do1 +4<<9,1

Sdud dojxpdv grhqêdv/ wdlv frpr dojxqv fåqfhuhv h vðqgurph gh Grzq/ d vxd

hwlrorjld dlqgd ì lqfhuwd h h{lvwh xpd vxvshlwd gh txh hodv srghp whu xpd fdxvd

lqihfflrvd1 Vh dvvlp irvvh/ hvshud0vh txh fdvrv suö{lprv qr whpsr whqghp d hvwdu

suö{lprv qr hvsdêr wdpeìp ghylgr dr surfhvvr gh wudqvplvvær hqyroylgr1 D

Page 12: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

4151 WLSRORJLD GRV GDGRV HVSDFLDLV :

x

y

590000 600000 610000 620000 630000

7850

0079

0000

7950

0080

0000

8050

0081

0000

Iljxud 414= Pdsd gh Ehor Krul}rqwh frp d srvlêær h{dwd gd uhvlgíqfld gh xpd

dprvwud gh 866 lqglyðgxrv grdgruhv gh vdqjxh qr pxqlfðslr1 Irqwh= Prqwhlur0gh0

Fdvwur hw do1 +5334,1

Page 13: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

; FDSÐWXOR 41 LQWURGXÊÆR

Iljxud 415= Pdsd sdufldo gh Ehor Krul}rqwh prvwudqgr dv orfdol}dêøhv h{dwdv gd

rfruuíqfld gh wrgrv fulphv ylrohqwrv qr dqr gh 4<<; uhjlvwudgrv shod Sroðfld Plolwdu1

Pdqfkdv flq}dv vær idyhodv/ Irqwh= SPPJ1

txhvwær ì txh fdvrv suö{lprv qr hvsdfr h whpsr whqghp d rfruuhu sru phur dfdvr

h dvvlp ì gh lqwhuhvvh txdqwl�fdu d hylgíqfld gh txh h{lvwh xp h{fhvvr gh hyhqwrv

suö{lprv vlpxodwdqhdphqwh qr hvsdfr h qr whpsr1

Qd Iljxud 416 yhprv xp pdsd el glphqvlrqdo hvtxhpäwlfr/ frp xp ulr dwudy0

hvvdqgr d äuhd h frp hyhqwrv +fdvrv gh xpd grhqêd, glvsrvwrv dr dfdvr1 Sdud fdgd

fdvr/ h{lvwh dvvrfldgd xpd yduläyho txh ì r prphqwr gd lqihfêær +rx gr uhjlvwur

rx gr lqðflr grv vlqwrpdv/ ghshqghqgr gd vlwxdêær,1 Hvwh whpsr ì prvwudgr qr

hl{r yhuwlfdo1 Revhuyd0vh txh fdvrv suö{lprv qr whpsr whqghp d hvwdu wdpeìp

suö{lprv qr hvsdêr1 Gh idwr/ vh shupxwävvhprv dr dfdvr dv vhwdv gh whpsr hqwuh

rv fdvrv/ hp jhudo revhuyduðdprv xpd phqru dvvrfldêær hqwuh hvwdv gxdv yduläyhlv/

d glvwåqfld whpsrudo h d glvwåqfld hvsdfldo/ hqwuh rv sduhv gh fdvrv1

Xp judqgh qýphur gh duwljrv whp vlgr hvfulwr vreuh hvwh sureohpd gh lqwhudêær

hvsdfr0whpsr +Dvvxqêær h Uhlv/ 5334> Ednhu/ 4<<9> Mdftxh}/ 4<<9d> Nqr{/ 4<97>

Nxoogrui h Kmdopduv/ 4<<<> Odzvrq h Ylho/ 4<<8> Pdqwho/ 4<9:,1

Page 14: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

4151 WLSRORJLD GRV GDGRV HVSDFLDLV <

Interação Espaço-Tempo

[

\

WHPSR

Iljxud 416= Pdsd hvtxhpäwlfr gh hyhqwrv frp whpsr gh lqðflr grv vlqwrpdv uhs0

uhvhqwdgr qr hl{r yhuwlfdo1

R prghor hvwdwðvwlfr eävlfr sdud hvwh wlsr gh gdgrv ì dojxpd irupd gh surfhvvr

srqwxdo/ d pdlruld gdv dsolfdêøhv hqyroyhqgr hp dojxp prphqwr xp surfhvvr

gh Srlvvrq hp gxdv glphqvøhv frp d ghqvlgdgh gh hyhqwrv sru xqlgdgh gh äuhd

yduldqgr qr hvsdêr1 Dv wìfqlfdv pdlv xvdgdv hqyroyhp d ixqêær N gh�qlgd sru

Ulsoh| +4<::, h vxdv prgl�fdføhv +Gljjoh/ 4<;6> Gljjoh h Urzolqjvrq/ 4<<7> Gljjoh

h Hoolrww/ 4<<8, h pìwrgrv gh vxdyld}dêær edvhdgrv hp nhuqhov +Elwkhoo/ 4<<3>

Nhovdoo h Gljjoh/ 4<<8> Nhovdoo h Gljjoh/ 4<<;,1 Ydprv gdu dshqdv xp uhvxpr

h{wuhpdphqwh vxflqwr gh dojxqv grv sulqflsdlv srqwrv wìfqlfrv hqyroylgrv qhvwh

wlsr gh gdgrv1

R prghor eävlfr ì dtxhoh hp txh dv srvlêøhv dohdwöuldv grv hyhqwrv qr pdsd

vær xpd uhdol}dêær gh xp surfhvvr gh Srlvvrq qær krprjíqhr frp ghqvlgdgh gh

hyhqwrv sru xqlgdgh gh äuhd ghqrwdgd sru �+{,/ rqgh { @ +{4> {5, uhsuhvhqwd d

srvlêær hvsdfldo1 Hvwlpdêær sru pä{lpd yhurvvlplokdqêd +Gljjoh/ 4<;6,/ rx xpd

yhuvær urexvwd +Dvvxqêær h Jxwwrus/ 4<<<,/ srgh vhu xvdgd1

Page 15: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

43 FDSÐWXOR 41 LQWURGXÊÆR

Vh �+{, uhsuhvhqwd d ghqvlgdgh srsxodflrqdo qd uhjlær gh hvwxgr/ hqwær

�+{, @ ��+{,�+{,

rqgh � ì xpd wd{d gh uhihuíqfld joredo sdud d grhqfd h �+{, ì d vxshuiðflh gh

ulvfr uhodwlyr hp uhodêær d hvwh ydoru gh uhihuíqfld1 R lqwhuhvvh xvxdo ì hvwlpdu r

orjdulwpr gr ulvfr uhodwlyr �+{, @ orj �+{,1 Fryduläyhlv dpelhqwdlv [l+{, phglgdv

vreuh wrgd d uhjlær srghp vhu lqwurgx}lgdv gh prgr txh prghorv wdlv frpr �+{, @

orj �+{, @ �3 . �4[4+{, . ===. �n[n+{, srghp vhu hvwxgdgrv1 Dojxqv whvwhv gh

lqwhuhvvh vær uhodflrqdgrv frp dv klsöwhvhv qxodv K3 = �+{, @ 3/ lvwr ì/ d ghqvlgdgh

gh fdvrv ì sursruflrqdo ã ghqvlgdgh srsxodflrqdo/ h K3 = �l @ 3/ r ulvfr uhodwlyr

qær hvwä dvvrfldgr frp d yduläyho dpelhqwdo [l+{,1

Xpd vlwxdêær suäwlfd pxlwr frpxp ì dtxhod hp txh h{lvwhp gdgrv vreuh q @

q4 . q5 hyhqwrv orfdol}dgrv qr pdsd fruuhvsrqghqwhv d q4 fdvrv gd grhqêd hp

srvlêøhv +{4> = = = >{q4 , h q5 fdvrv gh xp juxsr gh lqglyðgxrv txh qær srvvxhp d

grhqêd h txh vhuyhp frpr juxsr gh frqwuroh orfdol}dgrv hp +{q4.4> = = = >{q,1 Xpd

irupd qær0sdudpìwulfd vlpsohv gh hvwlpdu d ixqêær gh ulvfr uhodwlyr ì dwudyìv gr

orj gd ud}ær gh nhuqhov=

a�+e{,� @ orj

# Sq4l@4N� +{� {l,Sq

[email protected]� +{� {l,

$rqgh N+�, ì dojxpd ixqêær nhuqho vlpìwulfd udgldophqwh h � ì d odujxud gh edqgd

+edqgzlgwk,1 Yhu Edloh| h Jdwuhoo +4<<8,/ Elwkho +4<<3, h Nhovdoo h Gljjoh+4<<8,1

Sdud hylwdu d gliðflo hvfrokd gh xpd odujxud gh edqgd öwlpd � / Nhovdoo h Glj0

joh +4<<;, dgrwdp xp pìwrgr edvhdgr qxpd uhjuhvvær elqäuld qær0sdudpìwulfd

dwulexlqgr ydoruhv |l elqäulrv d fdgd xpd grv q hyhqwrv gr pdsd/ |l @ 4 vh r

hyhqwr ì xp fdvr h |l @ 3/ fdvr frqwuäulr1 D suredelolgdgh !+{, gh txh xp hyhqwr

txdotxhu ì xp fdvr ì hvwlpdgd yld uhjuhvvær sru nhuqho +Juhhq h Vloyhupdq/ 4<<7,

gh |l hp {l=

a!+{, @

Sq

l@4N� +{ � {l,|lSq

l@4N� +{ � {l,D phqrv gh xpd frqvwdqwh dglwlyd/ a�+{, @ orj

�a!+{,@+4� a!+{,,

�1 Pìwrgrv gh

vhohêær gh odujxud gh edqgd vær pxlwr pdlv vlpsohv qhvwd derugdjhp h/ doìp

Page 16: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

4151 WLSRORJLD GRV GDGRV HVSDFLDLV 44

glvwr/ hvwh pìwrgr shuplwh d lqwurgxêær gh fryduläyhlv dr qðyho lqglylgxdo/ wdlv

frpr lgdgh h vh{r yld prghorv jhqhudol}dgrv dglwlyrv +JDP,1

41515 Gdgrv gh vxshuiðflh dohdwöuld

Ghqwur ghvwd fdwhjruld gh gdgrv hqfrqwud0vh xpd lphqvd txdqwlgdgh gh wudedokr

sxeolfdgr1 Hqfdl{d0vh dtxl wrgd d äuhd fkdpdgd gh jhrhvwdwðvwlfd1 R txh glvwlqjxh

hvwh wlsr gh gdgr ì r txh ì frqvlghudgr dohdwöulr= dohdwöulr ì d vxshuiðflh ]+{, gr

ihq÷phqr hvwxgdgr +vxshuiðflh gh whpshudwxud/ dflgh} gr vror/ sk gd äjxd gh xp

odjr/ hwf1,1 Jhudophqwh/ h{lvwhp q hvwdêøhv gh frohwd gh gdgrv hp orfdol}dêøhv �{dv

+{4> = = = >{q,1 Qhvwdv hvwdêøhv/ d vxshuiðflh ]+{, ì revhuydgd h{dwdphqwh jhudqgr

dv yduðyhlv dohdwöuldv +]+{4,> = = = > ]+{q,, fxmd glvwulexlêær frqmxqwd ì lqgx}lgd shod

glvwulexlêær gd vxshuiðflh dohdwöuld ]+{,1 Ì öeylr txh sursulhgdghv vlpsohv wdlv

frpr frqwlqxlgdgh gd vxshuiðflh dohdwöuld yær lqgx}lu frydulåqfldv hqwuh dv ydu0

läyhlv dohdwöuldv +]+{4,> = = = > ]+{q,,1 Dojxpdv yh}hv/ revhuyd0vh d vxshuiðflh frp

dojxp huur gh phglêær r txdo jhud r fkdpdgr hihlwr gh shslwd1

Dojxqv grv sureohpdv wðslfrv hvwxgdgrv frp hvwh wlsr gh gdgrv vær= suhgl}hu d

vxshuiðflh hp orfdol}dêøhv qær prqlwrudgdv/ id}hu xpd lqwhusrodêær sdud uhfxshudu

d vxshuiðflh d sduwlu gd revhuydêær ghvwd dshqdv qdv hvwdføhv gh frohwd/ h hvfrokhu

xpd orfdol}dêær sdud vhgldu xpd qryd hvwdêær gh frohwd1

D Iljxud 417 prvwud xpd vxshuiðflh dohdwöuld frp hvwdføhv gh frohwd pdufdgdv

sru vhwdv h xpd orfdol}dêær rqgh ghvhmd0vh suhgl}hu r ydoru qær revhuydgr gd

vxshuiðflh pdufdgd sru udlr1

Revhuyh txh hvwdv hvwdêøhv gh frohwd vær srqwrv qr pdsd pdv r surfhvvr txh

jhurx r vhx srvlflrqdphqwr qr pdsd qær ì gh lqwhuhvvh/ glihuhqwhphqwh grv sur0

fhvvrv srqwxdlv1 Hp jhudo/ hvwdv hvwdêøhv gh frohwd vær hvfroklgdv h srvlflrqdgdv

gh dfrugr frp ghflvøhv jhuhqfldlv1 Phvpr qr fdvr hp txh hodv vær hvfroklgdv sru

dojxp phfdqlvpr dohdwöulr/ hvwh ýowlpr qær ì gh lqwhuhvvh/ h dvvlp dv hvwdføhv vær

frqvlghudgdv �{dv h wrgd lqihuíqfld ì ihlwd frqglflrqdophqwh hp vxdv srvlêøhv1

Nuljdjhp ì r pìwrgr fkdyh sdud hvwh wlsr gh gdgr/ edvlfdphqwh xp prghor gh

uhjuhvvær frp huurv fruuhodflrqdgrv shod glvwåqfld hqwuh dv hvwdêøhv gh frohwd1 D

Page 17: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

45 FDSÐWXOR 41 LQWURGXÊÆR

Dados de Superfícies Aleatórias

(VWDo}HV GH FROHWD QDV ORFDo}HV PDUFDGDV SRU

7HPSHUDWXUD� 3K GH iJXD GH ODJR� DFLGH] GR VROR���

/RFDOL]DomR D SUHGL]HU� PDUFDGD SRU

Iljxud 417= Vxshuiðflh dohdwöuld frp hvwdêøhv gh frohwd pdufdgdv sru vhwdv h or0

fdol}dêær rqgh ghvhmd0vh suhgl}hu r ydoru qær revhuydgr gd vxshuiðflh pdufdgr sru

udlr1

Page 18: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

4151 WLSRORJLD GRV GDGRV HVSDFLDLV 46

fruuhodêær grv huurv ì gh�qlgd d sduwlu gh xp ydulrjudpd/ xpd ixqêær txh phgh

r judx gh lqghshqgíqfld hqwuh rv huurv gh dfrugr frp glvwåqfld1

Uhfhqwhphqwh/ krxyh xp plqlfxuvr qr VLQDSH gdgr sru Shwhu Gljjoh h Sdxor

Ulehlur wrwdophqwh ghglfdgr d hvwh wlsr gh gdgr1 Hvwh plqlfxuvr xwlol}rx r olyur

Prgho Edvhg Jhrvwdwlvwlfv +Gljjoh h Ulehlur/ 5333, txh srgh vhu dgtxlulgr mxqwr

d DEH h txh uhfrphqgdprv iruwhphqwh drv ohlwruhv lqwhuhvvdgrv qhvvh dvvxqwr1

41516 Gdgrv gh äuhd

Hvwh wlsr gh gdgr jhudophqwh srgh vhu ylvxdol}dgr hp pdsdv rqgh r hvsdfr ì

sduwlflrqdgr hp äuhdv h fdgd äuhd ì frorulgd gh dfrugr frp dojxpd yduläyho1 D

glylvær jhrjuä�fd srgh uhsuhvhqwdu glylvøhv dgplqlvwudwlydv gh fduäwhu sroðwlfr rx

dgplqlvwudwlyr rx glylvøhv ihlwdv frp edvh hp fdudfwhuðvwlfdv jhriðvlfdv wdlv frpr

}rqdv folpäwlfdv1

H{hpsor= D Iljxud 418 prvwud xp pdsd gh wd{dv gh pruwdolgdgh sru fåqfhu gh

sxopær qrv Hvwdgrv Xqlgrv sru frqgdgr/ sdud krphqv eudqfrv hp 4<<;1 Hvwh

pdsd irl surgx}lgr shor Fhqwhu iru Glvhdvh Frqwuro +FGF,1 Hoh prvwud txh dowdv

wd{dv srghp vhu hqfrqwudgdv qdv äuhdv txh �fdp dr orqjr grv ydohv grv ulrv

Plvvlvvlsl h Rklr1 Hvwh sdguær uh hwh r dowr frqvxpr shu fdslwd gh fljduurv qhvwdv

äuhdv/ mä txh r fljduur ì r sulqflsdo idwru gh ulvfr sdud r fåqfhu gh sxopær1

Dvvlp/ rv gdgrv gh äuhd vær uhsuhvhqwdgrv sru xp yhwru +|4> ===> |q, rqgh fdgd

xp grv ydoruhv |l hvwä dvvrfldgr frp xpd gdv äuhd l gr pdsd1 D sulqflsdo fdu0

dfwhuðvwlfd ghvwh wlsr gh gdgr ì txh hoh uhsuhvhqwd xpd djuhjdêær gh ydoruhv txh

hqfrqwudp0vh glvshuvrv ghqwur gh fdgd xpd gdv äuhdv1 Lvwr ì/ |l qær vh uhihuh d

qhqkxpd srvlêær hvshfð�fd ghqwur gd äuhd lpdv/ qd yhugdgh/ hvwä dvvrfldgr d wrgd

d äuhd l hp txhvwær1 Dv äuhdv srghp wdpeìp uhsuhvhqwdu xpd judgh uhjxoduphqwh

hvsdêdgd wdo frpr hp lpdjhqv gh vdwìolwh rx irwrjud�dv1 Hvwh olyur hvwduä frq0

fhqwudgr hp wìfqlfdv gh dsolfdêær pdlv frpxp hp äuhdv gdv flíqfldv vrfldlv h gh

vdýgh wdlv frpr hslghplrorjld/ hfrqrpld h ghprjud�d h dvvlp/ ydprv frqvlghudu

judghv luuhjxoduhv wdo frpr dtxhodv irupdgdv sru glylvøhv sroðwlfr0dgplqlvwudwlydv1

Hperud r ydoru |l hvwhmd dvvrfldgr d wrgd d äuhd/ dojxpdv wìfqlfdv uhtxhuhp

dojxp srqwr gh uhihuíqfld ghqwur gr sroðjrqr irupdgr shod äuhd sdud orfdol}du r

Page 19: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

47 FDSÐWXOR 41 LQWURGXÊÆR

Iljxud 418= Pdsd gdv wd{dv gh fåqfhu gh sxopær qd srsxodêær eudqfd pdvfxolqd

grv Hvwdgrv Xqlgrv/ sru frqgdgrv1 Irqwh= Fhqwhu iru Glvhdvh Frqwuro1

ydoru1 Hp jhudo/ ì hvfroklgr r fhqwuölgh gd äuhd1 Qr hqwdqwr/ revhuyh txh/ yld gh

uhjud/ qær id} vhqwlgr shqvdu hp lqwhusrodêær hp srqwrv qær revhuydgrv mä txh

qær kä ydoruhv �hqwuh dv äuhdv�1

Dojxqv grv sulqflsdlv lqwhuhvvhv dr id}hu lqihuíqfldv vreuh r sdguær hvsdfldo

revhuydgr vær= whvwdu vh r sdguær ì dohdwöulr> rewhu pdsdv pdlv vxdyhv txh r pdsd

revhuydgr/ surfxudqgr hvwlpdwlydv phokruhv gh hvwuxwxudv vxemdfhqwhv> ghwhfwdu

vxe0uhjløhv gh ydoruhv pdlv hohydgrv gr txh r hvshudgr vre dojxp prghor h prghorv

gh uhjuhvvær hvsdfldo1 Hvwhv vær rv wöslfrv grv fdsðwxorv vhjxlqwhv ghvwh olyur1

41517 Gdgrv gh lqwhudêær hvsdfldo

Qhvwh wlsr gh gdgr qöv wdpeìp whprv hvwdêøhv rx srvlêøhv �{dv/ wdo frpr hp

gdgrv gh vxshuiðflhv dohdwöuldv1 Hqwuhwdqwr/ hvwdv hvwdêøhv vær frqvlghudgdv frpr

sduhv rughqdgrv/ vhqgr txh xp grv hohphqwrv gr sdu ì frqvlghudgr xpd ruljhp

hqtxdqwr r rxwur ì xp ghvwlqr1 R txh wudihjd hqwuh hvwhv sduhv ì xp x{r h ì hvwh

Page 20: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

4161 D SUÄWLFD GD DQÄOLVH GH GDGRV HVSDFLDLV 48

x{r txh ì dohdwöulr1 Dvvlp/ r gdgr dohdwöulr txh ghyh vhu prghodgr ì gd irupd

|lm uhsuhvhqwdqgr xp x{r gd hvwdêær l sdud d hvwdêær m1 H{hpsorv frpxqv vær

rv gdgrv gh x{r pljudwöulr/ r x{r gh sdflhqwhv hqwuh fhqwurv gh dwhqglphqwr/ r

x{r gh sdvvdjhlurv hqwuh flgdghv/ r x{r gh whohirqhpdv hqwuh wruuhv gh fdswdfær

gh vlqdlv/ hwf1

Rv sureohpdv wðslfrv txh dsduhfhp txdqgr hvwh wlsr gh gdgr dohdwöulr ì frq0

vlghudgr vær= frpr h txdlv dv fdudfwhuðvwlfdv revhuyäyhlv gdv hvwdêøhv +wdpdqkr/

wlsr/ hwf1, ghwhuplqdp r yroxph gr x{r hqwuh hvwdêøhv> rqgh frorfdu xpd qryd

hvwdêær sdud plqlpl}du r fxvwr joredo gr x{r/ hwf1

Xp prghor wudglflrqdo ì r judylwdflrqdo rqgh r ydoru pìglr gr x{r hqwuh l h

m ì xp surgxwr gh fdudfwhuðvwlfdv gd hvwdêær l/ gh fdudfwhuðvwlfdv gd hvwdêær m h

gd glvwåqfld hqwuh l h m/ srvvlyhophqwh frp fryduläyhlv dglflrqdgdv d hvwd phglgd

gh glvwåqfld1 Xp prghor orj0olqhdu ì r srqwr gh sduwlgd frp

orj+�lm, @ j+fdudfwhuðvwlfdv gh l, . j+fdudfwhuðvwlfdv gh m, . �k+glm,

rqgh �lm @ H+|lm, h glm ì xpd phglgd gh glvwåqfld hqwuh l h m1

Hperud kdmd xpd hqruph olwhudwxud uhodflrqdgd frp hvwh wlsr gh gdgr/ hod hvwä

frqfhqwudgd qdv pærv gh hfrqrplvwdv h jhöjudirv/ vhqgr d suhvhqfd gh hvwdwðvwlfrv

shtxhqd1 1 D Iljxud 419 prvwud xp h{hpsor hvtxhpäwlfr gh gdgrv gh lqwhudêær

hvsdfldo1

416 D suäwlfd gd dqäolvh gh gdgrv hvsdfldlv

Sdud fdgd xp ghvwhv txdwur wlsrv gh gdgrv hvsdfldlv/ h{lvwhp pìwrgrv hvwdwðvwl0

frv glihuhqwhv txh srghp vhu xvdgrv sdud ghvfuhyhu rx id}hu lqihuíqfld vreuh rv

sduåphwurv dvvrfldgrv drv prghorv1 Qhvwh olyur qöv ydprv qrv frqfhqwudu hp dsh0

qdv xp wlsr gh gdgr hvsdfldo/ rv gdgrv gh äuhd1 Doìp glvwr/ ydprv xvdu pxlwrv

h{hpsorv gdv äuhdv gh vdýgh h vrfldo/ dv sulqflsdlv äuhdv gh dwxdêær ghvwh dxwru1

Hp sduwlfxodu/ rv h{hpsorv xwlol}dgrv yluær sulqflsdophqwh gd hslghplrorjld/ txh

whp frqwulexðgr frp pxlwrv grv sureohpdv dwdfdgrv shorv hvwdwðvwlfrv/ ehp frpr

surslfldgr r ghvhqyroylphqwr gh pìwrgrv lpsruwdqwhv gh hvwdwðvwlfd1 Hvwd lqwhu0

Page 21: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

49 FDSÐWXOR 41 LQWURGXÊÆR

Dados de Interação Espacial&tUFXORV 0XQLFtSLRV GH UHJLmR HP 0* HP ����

�5DLR SURSRUFLRQDO DR WDPDQKR

GD SRSXODomR

5RWD DpUHD

/DUJXUD GD URWD p

SURSRUFLRQDO DR IOX[R

GH SDVVDJHLURV

Iljxud 419= H{hpsor gh gdgrv gh lqwhudfdr hvsdfldo1

dêær hqwuh hvwdwðvwlfd hvsdfldo h hslghplrorjld uhshwh d iuxwðihud lqwhudêær frp d

äuhd gh vdýgh sýeolfd hp rxwudv äuhdv gd hvwdwðvwlfd1

Yäulrv qýphurv grv sulqflsdlv shulöglfrv gh hslghplrorjld h gh hvwdwðvwlfd wíp

dsuhvhqwdgr pìwrgrv gh hvwdwðvwlfd hvsdfldo hp hslghplrorjld +sru h{hpsor/ Dphu0

lfdq Mrxuqdo ri Hslghplrorj|/ 465= V40V535/ 4<<31 Mrxuqdo ri Ur|do Vwdwlvwlfdo Vr0

flhw|/ Vhulhv D/ 485/ 4<;<1 Mrxuqdo ri Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv G/ 7:/ 4<;<1

Vwdwlvwlfv lq Phglflqh= 45/ 4<<6> 48/ 4<<9> 47/ 4<<8,1 Yäulrv olyurv wíp dsduhfl0

gr xowlpdphqwh wrwdophqwh ghyrwdgrv d hvwd äuhd +sru h{hpsor/ Edloh| h Jdwuhoo/

4<<8> Odzvrq hw do/ 4<<<d> Jdwuhoo h Or|wrqhq/ 4<<;> Kdoorudq h Juhhqkrxvh/ 4<<:>

Hoolrw hw do/ 4<<9,1

Yäuldv lqlfldwlydv lqwhuqdflrqdlv wíp prelol}dgr hvwdwðvwlfrv hp wruqr gh hv0

wdwðvwlfd hvsdfldo1 R h{fhohqwh olyur gh Odzvrq hw do +4<<<d, ì uhvxowdgr gh xp

zrunvkrs lqwhuqdflrqdo vreuh pdshdphqwr gh grhqêdv h dydoldêær gh ulvfrv/ uh0

dol}dgr hp Urpd hp 4<<:/ vre rv dxvsðflrv gd Rujdql}dêær Pxqgldo gh Vdýgh

+ZKR,/ gr Hxurshdq Fhqwuh iru Hqylurqphqw dqg Khdowk h gd Xqlær Hxursìld1

Page 22: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

4161 D SUÄWLFD GD DQÄOLVH GH GDGRV HVSDFLDLV 4:

R olyur Hoolrw hw do +4<<9, irl uhvxowdgr gh xpd lqlfldwlyd dqwhulru gr phvpr irupd0

wr1 Doìp glvwr/ xpd judqgh txdqwlgdgh gh wudedokr hvwdwðvwlfr whp vlgr uhdol}dgr

hp/ rx frp r dsrlr �qdqfhlur gh/ lqvwlwxlêøhv lqwhuvvdgdv hp sureohpdv dvvrfl0

dgrv frp vdýgh h phlr dpelhqwh wdlv frpr= X1V1 Fhqwuhv iru Glvhdvh Frqwuro

dqg Suhyhqwlrq +FGF,> X1V1 Hqylurqphqwdo Surwhfwlrq Djhqf| +HSD,> X1V1 Qd0

wlrqdo Uhvhdufk Fhqwuh iru Vwdwlvwlfv dqg wkh Hqylurqphqw> Sdq Dphulfdq Khdowk

Rujdql}dwlrq +SDKR,> Zruog Khdowk Rujdql}dwlrq +ZKR,/ hqwuh rxwudv1

Hp vrflrorjld/ d sulqflsdo äuhd gh ghvhqyroylphqwr h xvr gh wìfqlfdv gh dqäolvh

hvsdfldo whp vlgr d dqäolvh gh fulphv1 R Qdwlrqdo Lqvwlwxwh ri Mxvwlfh whp �qdfldgr

yäulrv surmhwrv h/ hp sduwlfxodu/ d fuldêær gh xp vriwzduh +FULPHVWDW , h xp

zhevlwh

+kwws=22zzz1rms1xvgrm1jry2fpuf2 ,

sdud glvvhplqdu d dqäolvh hvsdfldo gh fulphv1 Xp frqjuhvvr dqxdo dshqdv vreuh

hvwh dvvxqwr whp vlgr uhdol}dgr dqxdophqwh qrv HXD h/ hp vhwhpeur25334/ d

XIPJ ydl vhgldu xp frqjuhvvr lqwhuqdflrqdo vreuh d dqäolvh hvsdfldo gh fulphv1

Qr Eudvlo h{lvwh pxlwr pdwhuldo glvsrqðyho sdud r shvtxlvdgru lqwhuhvvdgr1 Hp

sulphlur oxjdu/ ì ixqgdphqwdo uhjlvwudu d h{lvwíqfld gr vriwzduh VSULQJ/ ghvhq0

yroylgr qr LQSH gh Vær Mrvì grv Fdpsrv/ h glvsrqðyho judwxlwdphqwh shod lqwhuqhw

+kwws=22zzz1lqsh1jry1eu,

qdv sodwdirupdv XQL[ h Zlqgrzv1 Hvwh vriwzduh ì xp Vlvwhpd Jhrjuä�fr gh

Lqirupdfær edvwdqwh srghurvr fdsd} gh olgdu frp xp judqgh yroxph gh lqirupd0

føhv h dwxdophqwh hvwä vhqgr lqfuhphqwdgr frp xp pögxor gh hvwdwðvwlfd hvsdfldo

yrowdgr sdud dsolfdføhv qd äuhd gh vdýgh1 Pdlruhv lqirupdføhv srghp vhu rewlgdv

qr hqghuhfr dflpd1

R Plqlvwìulr gd Vdýgh h d Uhsuhvhqwdêær gd RSDV qr Eudvlo fuldudp d ULSVD

+Uhgh Lqwhudjhqfldo gh Lqirupdêøhv sdud d Vdýgh,/ fxmr hqghuhêr hohwu÷qlfr ì

kwws=22zzz1vdxgh1jry1eu2lqirup2ulsvd1kwp1

Hvvd uhgh whp frpr sursövlwr d glvsrqlelol}dêær dghtxdgd/ rsruwxqd h deudqjhqwh

gh gdgrv eävlfrv/ lqglfdgruhv h dqäolvhv gh vlwxdêær vreuh dv frqglêøhv gh vdýgh

h vxdv whqgíqfldv qr sdðv/ frp ylvwdv dr dshuihlêrdphqwr gd fdsdflgdgh gh iru0

pxodêær/ frrughqdêær/ jhvwær h rshudflrqdol}dêær gh sroðwlfdv h dêøhv sýeolfdv

Page 23: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

4; FDSÐWXOR 41 LQWURGXÊÆR

gluljlgdv ã txdolgdgh gh vdýgh h gh ylgd gd srsxodêær1

R Plqlvwìulr gd Vdýgh glvsrqlelol}d gh irupd judwxlwd qr hqghuhêr

kwws=22zzz1gdwdvxv1jry1eu2wdezlq2wdezlq1kwp

r vriwzduh Wdezlq h dutxlyrv sdud Wdezlq gh pdsdv sdud r Eudvlo/ frp glylvøhv

dwì r qðyho gh pxqlfðslrv1 Hvvh vriwzduh srvvlelolwd gh irupd edvwdqwh dfhvvðyho d

frqihfêær gh pdsdv whpäwlfrv frp lqirupdêøhv gh vdýgh gh hvwdgrv/ uhjløhv h

pxqlfðslrv eudvlohlurv1

Xpd olvwd gh glvfxvvær gh sureohpdv gh dqäolvh gh gdgrv hvsdfldlv hp vdýgh

fkdpdgd DGHV0O irl fuldgd sru shvtxlvdgruhv gd ILRFUX] h gr Surjudpd gh

Hqjhqkduld Elrpìglfd2FRSSH2XIUM1 Rv sulqflsdlv dvvxqwrv gh lqwhuhvvh vær=

pìwrgrv hvwdwðvwlfrv dsolfdgrv d dqäolvhv hvsdfldlv h hvsdêr0whpsrudlv> pìwrgrv gh

dqäolvh hp plfur0äuhdv> edvhv fduwrjuä�fdv h jhruhihuhqfldphqwr gdv lqirupdêøhv>

VLJ dsolfdgr ã vdxgh> hslghplrorjld hvsdfldo h glyxojdêær gh hyhqwrv uhodflrqdgrv

dr whpd1 R hqghuhêr gd olvwd ì

kwws=22zzz1hqvs1�rfux}1eu2vhuylfrv2dghv0o1kwpo1

Sdud vh lqvfuhyhu qd olvwd edvwd hqyldu h0pdlo +vhp vxemhfw, d sduwlu gd frqwd

txh yrfh ghvhmd fdgdvwudu sdud uhfhehu dv phqvdjhqv/ sdud r vhjxlqwh hqghuhêr=

pdmrugrprCpdoduld1surff1�rfux}1eu1

Qr frusr gd phqvdjhp ghyh frqvwdu dshqdv r vhjxlqwh wh{wr= VXEVFULEH

DGHV0O Lqirupdêøhv dglflrqdlv srghp vhu rewlgdv qr hqghuhêr flwdgr1

Doìp glvvr/ xwlol}dqgr txdotxhu vlvwhpd gh exvfd qd lqwhuqhw srgh0vh hqfrqwudu

xpd judqgh txdqwlgdgh gh olqnv gh xwlolgdgh sdud r shvtxlvdgru lqwhuvvdgr hp

hvwdwðvwlfd hvsdfldo1

417 Vlvwhpdv Jhrjuä�frv gh Lqirupdêær h Hvwdwðv0

wlfd Hvsdfldo

R xvr gh pdsdv/ sduwlfxoduphqwh vh lqirupdwl}dgrv/ srgh wruqdu pdlv hihwlyd d

wrpdgd gh ghflvøhv1 D Rujdql}dfær Sdq0dphulfdqd gh Vdýgh hvwlpd txh fhufd gh

;3( gdv qhfhvvlgdghv gh lqirupdêøhv gdv shvvrdv txh wrpdp ghflvøhv h gh�qhp

Page 24: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

4171 VLVWHPDV JHRJUÄILFRV GH LQIRUPDÊÆRH HVWDWÐVWLFD HVSDFLDO4<

sroðwlfdv qrv jryhuqrv orfdlv hvwær uhodflrqdgdv frp d orfdol}dêær jhrjuä�fd1

Xp Vlvwhpd gh Lqirupdêær Jhrjuä�fd +VLJ, ì xp frqmxqwr gh htxlsdphqwrv h

surjudpdv gh frpsxwdêær txh lqwhjudp pdsdv h juä�frv frp xpd edvh gh gdgrv

vreuh xp hvsdêr jhrjuä�fr gh�qlgr/ rx vhmd/ xp frqmxqwr gh ihuudphqwdv fdsd}hv

gh frohwdu/ dupd}hqdu/ pdqhmdu/ dqdolvdu h ylvxdol}du lqirupdêøhv jhruhihuhqfldgdv1

D pdlru gl�fxogdgh sdud d xwlol}dfær hihwlyd gd lqirupdfær jhruhihuhqfldgd qxp

JLV ì d fuldfær gh vxdv edvhv gh gdgrv1

Qr Eudvlo/ mä h{lvwh pxlwd lqirupdfdr vrfldo h hfrq÷plfd glvsrqðyho hp xqlgdghv

jhrjuä�fdv edvwdqwh ghwdokdgdv sdud r shvtxlvdgru lqwhuhvvdgr1 R Lqvwlwxwr Eudvlohlur

gh Jhrjud�d h Hvwdwðvwlfd/ LEJH/ ì r ghsrvlwäulr gd pdlru irqwh gh lqirupdêøhv

vrfldlv h hfrq÷plfdv vreuh r sdðv1 Doìp gh xpd lphqvd txdqwlgdgh gh gdgrv gh

rxwudv shvtxlvdv/ r LEJH glvsrqlelol}d lqirupdêøhv fhqvlwäuldv ghwdokdgdv vreuh d

srsxodêær eudvlohlud hp shtxhqdv äuhdv fkdpdgdv vhwruhv fhqvlwäulrv1 R vhwru ì

d phqru xqlgdgh jhrjuä�fd sdud d txdo gdgrv srsxodflrqdlv +vre d irupd gh ydo0

ruhv pìglrv rx sursruêøhv, srghp vhu wruqdgrv sýeolfrv1 R frqmxqwr gh vhwruhv

fhqvlwäulrv freuh wrgd d h{whqvær whuulwruldo eudvlohlud/ xuedqd rx uxudo/ h hvwä dvvr0

fldgd frp d rshudêær gh frohwd gh gdgrv grv Fhqvrv Ghprjuä�frv uhdol}dgrv shor

LEJH d fdgd gh} dqrv1 Gh irupd jhqìulfd/ rv vhwruhv fhqvlwäulrv fruuhvsrqghp d

xpd äuhd jhrjuä�fd wdo txh rv vhxv grplfðolrv frpsrqhqwhv srghp vhu olvwdgrv hp

xp gld gh wudedokr sru xpd ýqlfd shvvrd sdud srvwhulru uhfhqvhdphqwr1 Gh irupd

phqrv ydjd/ rv vhwruhv fhqvlwäulrv yduldp hp whuprv gh äuhd h gh srsxodêær1 Frp0

sdudgr frp äuhdv xuedqdv/ rv vhwruhv gh äuhdv uxudlv whqghp d vhu pxlwr pdlruhv

hp whuprv gh h{whqvær whuulwruldo h pxlwr phqruhv hp whuprv gh srsxodêær frp0

srqhqwh1 Hp äuhdv xuedqdv/ rv vhwruhv srvvxhp hp pìgld 633 grplfðolrv/ frp

<3( ghohv yduldqgr hqwuh 433 h 833 grplfðolrv/ dsur{lpdgdphqwh1

D pdokd jhrjuä�fd grv vhwruhv fhqvlwäulrv eudvlohlurv/ wdqwr xuedqrv txdqwr

uxudlv/ hvwä sudwlfdphqwh surqwd pdv dlqgd qær hvwä glvsrqðyho sdud r judqgh

sýeolfr1 Wrgrv rv pxqlfðslrv frp srsxodfær dflpd gh 433 plo kdelwdqwhv hvwær

surqwrv h r uhvwdqwh hvwä hp idvh �qdo1 Xpd gdv pdlruhv gl�fxogdghv wìfqlfdv ì

id}hu frp txh dv pdokdv gh grlv rx pdlv pxqlfðslrv yl}lqkrv fuldgrv vhsdudgd0

phqwh vhmdp frpsdwðyhlv hqwuh vl gh prgr txh xp xvxäulr srvvd wudedokdu frp

Page 25: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

53 FDSÐWXOR 41 LQWURGXÊÆR

xp pdsd gh xpd uhjlær txh hqjoreh vhwruhv gh pxqlfðslrv glihuhqwhv1 Hvshud0

vh sdud pxlwr euhyh d �qdol}dfær ghvwh hqruph wudedokr qr LEJH1 Dvvlp/ wrgd

d ultxh}d gd lqirupdfær fhqvlwäuld qxpd hvfdod edvwdqwh ghwdokdgd hvwduä euhyh0

phqwh glvsrqðyho sdud rv shvtxlvdgruhv lqwhuhvvdgrv1 Doìp glvwr/ yäulrv vlvwhpdv

gh lqirupdfær gh rujærv sýeolfrv mä hvwær oljdgrv d hvwd edvh ghprjuä�fd1 Sru

h{hpsor/ rv yäulrv vlvwhpdv gh lqirupdêær hp vdýgh qdflrqdlv ghyhuær qr ixwxur

shuplwlu r jhruuhihuhqfldphqwr sdud vhwruhv fhqvlwäulrv +ULSVD/ 4<<<,1

Hp rxwurv sdðvhv h{lvwhp gh�qlêøhv vhphokdqwhv d grv vhwruhv fhqvlwäulrv/ wr0

grv mä jhruhihuhqfldgrv sdud xvr sru lqvwlwxlføhv sýeolfdv rx sulydgdv1 Qr Uhlqr

Xqlgr h{lvwhp rv Hqxphudwlrq Glvwulfwv/ deuhyldgrv sru HG/ txh srvvxhp/ hp

pìgld/ 733 lqglyðgxrv1 Pxlwrv hvwxgrv gh hvwdwðvwlfd hvsdfldo id}hp xvr ghvwhv

gdgrv1 Sru rxwur odgr/ hp hvwxgrv hslghplroöjlfrv/ lqirupdêøhv vreuh r orfdo gh

uhvlgíqfld gh grhqwhv rx gh pruwrv sru fdxvd hvshfð�fd gh pruwdolgdgh srghp vhu

rewlgdv id}hqgr xvr gr fögljr gh hqghuhfdphqwr srvwdo lqjoív/ r FHS lqjoív/ txh

ì fkdpdgr gh srvwfrgh gdwdedvh rx }lsfrgh gdwdedvh1 Hvwd edvh gh gdgrv ì pxlwr

pdlv ghwdokdgd jhrjud�fdphqwh txh d grv HGv freulqgr/ hp pìgld/ 48 grplfðolrv

+rx dsur{lpdgdphqwh 73 shvvrdv, fdgd xp1

Dwxdophqwh/ dojxpdv judqghv flgdghv eudvlohludv/ frpr Sruwr Dohjuh h Ehor

Krul}rqwh/ srghprv jhruhihuhqfldu wrgd d lqirupdfær uhjlvwudgd gd äuhd gh vdýgh

rx gd sroðfld plolwdu dr qðyho srqwxdo1 Lvwr ì/ rv hyhqwrv gh vdýgh rx rv fulphv

srghp vhu frorfdgrv qxp pdsd qd srvlfær h{dwd fruuhvsrqghqwh dr vhx hqghuhfr

h qær frpr frqwdjhqv djuhjdgdv ghqwur gh äuhdv1 Hvshudprv txh hp euhyh rxwudv

flgdghv eudvlohludv wdpeìp hvwduær frp vlvwhpdv vhphokdqwhv1

Page 26: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

Fdsðwxor 5

������ �� ����� �� ���

514 Lqwurgxêær

Hvwduhprv wudedokdqgr qr uhvwdqwh ghvwh wh{wr frp gdgrv gh äuhd1 Frpr h{sol0

fdprv dqwhulruphqwh/ hvwhv gdgrv uhihuhp0vh d xp pdsd sduwlflrqdgr hp äuhdv

frqwðjxdv h glvmxqwdv h/ hp fdgd xpd ghodv/ phghp0vh xpd rx pdlv yduläyhlv

dohdwöuldv |l h srvvlyhophqwh fryduläyhlv gh lqwhuhvvh h txh vxsrvwdphqwh dihwdp d

glvwulexlêær gh suredelolgdgh gh |l1

Hperud r ydoru |l hvwhmd dvvrfldgr frp wrgd d äuhd h qær frp xp srqwr

sduwlfxodu ì ýwlo ãv yh}hv dvvrfldu hvwh ydoru frp xp srqwr hvshfð�fr ghqwur gd

äuhd1 Xvxdophqwh hvwh srqwr ì r fhqwuölgh/ r fhqwur gh pdvvd gr sroðjrqr txh

gholqhld d äuhd1 Ãv yh}hv/ hoh wdpeìp frvwxpd vhu gh�qlgr frpr r srqwr dvvrfldgr

frp d vhgh gh xp pxqlfðslr1

515 Pdwul} gh shvrv hvsdfldlv

Ì xvxdo ghvfuhyhu d hvwuxwxud hvsdfldo gdv q xqlgdghv jhrjuä�fdv dwudyìv gh xpd

pdwul} txdgudgd q � q gh shvrv/ ghqrwdgd sru Z / rqgh zll @ 31 Rv hohphqwrv

zlm � 3 phghp r judx gh sur{lplgdgh jhrjuä�fd gdv äuhdv l h m1 D hvfrokd grv

hohphqwrvzlm ì duelwuäuld h ghyhuld vhu ihlwd ohydqgr0vh hp frqvlghudfdr r sureohpd

54

Page 27: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

55 FDSÐWXOR 51 DQÄOLVH GH GDGRV GH ÄUHD

hvshfl�fr vre dqdolvh1 Dohp glvwr/ d pdwul} Z srgh vhu dvvlpìwulfd hp dojxpdv

vlwxdêøhv1 Sru h{hpsor/ zlm srgh vhu sursruflrqdo d glvwåqfld fduwhvldqd hqwuh rv

fhqwurv srsxodflrqdlv rx jhrjuä�frv gdv äuhdv l h m rx srgh vhu sursruflrqdo dr

x{r gh shvvrdv uhvlghqwhv hp l txh wudedokdp hp m rx sursruflrqdo dr x{r gh

whohirqhpdv sduwlqgr gh uhvlgíqfldv hp l h frpxqlfdqgr0vh frp uhvlgíqfldv hp m1

Hvwhv x{rv srghp vhu fdofxodgrv frpr ydoruhv devroxwrv rx frpr ydoruhv uhodwlyrv

dr wrwdo gh fdgd äuhd1 Revhuyh txh qr fdvr ghvvhv x{rv hqwuh äuhdv/ zlm srgh vhu

glihuhqwh gh zml1

Xpd gdv hvfrokdv pdlv frpxqv sdud d pdwul} Z ì wrpdu dshqdv xpd pdwul}

elqäuld frp zlm @ 4 vh dv äuhdv l h m frpsduwlokdp iurqwhludv h zlm @ 3/ fdvr

frqwuäulr/ surgx}lqgr xpd pdwul} vlpìwulfd1 Vlphwuld gh Z ì lpsruwdqwh hp

dojxqv prghorv gh uhjuhvvær hvsdfldo/ frpr yhuhprv1 Xpd pdwul} dvvlpìwulfd

vhpsuh srgh vhu wudqvirupdgd qxpd vlpìwulfd vlpsohvphqwh uhgh�qlqgr qryrv

shvrv z�lm @ +zlm . zml,@51

Rxwudv hvfrokdv frpxqv sdud d pdwul} gh shvrv Z srghp vhu dv vhjxlqwhv=

� zlm @ 4 vh r fhqwuölgh gd äuhd m ì xp grv n fhqwuölghv pdlv suö{lprv gdtxhoh

gd äuhd l h 3/ fdvr frqwuäulr1

� zlm @ 4 vh r fhqwuölgh gd äuhd m glvwd phqrv txh n txlo÷phwurv gr fhqwuölgh

gd äuhd l h 3/ fdvr frqwuäulr1

� zlm @ g�lm rqgh glm ì d glvwåqfld hqwuh rv fhqwuölghv gdv äuhdv l h m=

� zlm @ g�

lm vh glm ? � h 3/ fdvr frqwuäulr1

Hp dojxqv fdvrv/ frvwxpd0vh sdgurql}du dv olqkdv gd pdwul} Z id}hqgr0vh

zl= @S

mzlm @ 41 Dvvlp/ rv shvrv zlm dvvrfldgrv frp d äuhd l vrpdp 41

516 Pdsdv frpr judirv

Ì edvwdqwh ýwlo uhsuhvhqwdu d lqirupdêær gh yl}lqkdqfd h shvr gh xp pdsd gh äuhdv

vre d irupd gh xp judir frp rv shvrv gd pdwul} Z uhsuhvhqwdgrv frpr shvrv gdv

duhvwdv gr judir1 Fdgd äuhd ì uhsuhvhqwdgd sru xp qö +rx srqwr,/ jhudophqwh

orfdol}dgr qr fhqwuölgh gd äuhd1 Txdqgr zlm A 3 h{lvwh xpd duhvwd frqhfwdqgr

Page 28: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

5161 PDSDV FRPR JUDIRV 56

coordenada x

coor

dena

da y

1 2 3 4 5 6

12

34

56 1

2 3

4 5

6

7

8

9

10

Grafo com Matriz Binaria

coordenada x

coor

dena

da y

1 2 3 4 5 6

12

34

56 1

2 3

4 5

6

7

8

9

10

Grafo com Matriz nao Binaria

Iljxud 514= Judir vlpsohv prvwudqgr r hvtxhpd gh xpd pdsd frpsrvwr sru 43

äuhdv1 R judir gd hvtxhugd dsuhvhqwd xpd vlwxdêær hp txh rv shvrv vær elqäulrv

h r gd gluhlwd dsuhvhqwd shvrv qær elqäulrv1

dv äuhdv l h m h/ vh zlm @ 3/ qhqkxpd duhvwd ì ghvhqkdgd1 D odujxud gdv duhvwdv

ì sursruflrqdo dr ydoru gh zlm 1 D Iljxud 514 prvwud xp h{hpsor vlpsohv gh 43

äuhdv fxmr pdsd irl uhsuhvhqwdgr frpr xp judir1 R judir gd hvtxhugd xvd xpd

pdwul} gh shvrv elqäuld h r judir gd gluhlwd xvd xpd pdwul} gh shvrv qdr elqduld1

Qrv pdsdv txh uhdophqwh hqfrqwudprv qdv dsolfdfrhv rv judirv whqghp d vhu

ehp pdlv frpsoh{rv1 D Iljxud 515 prvwud r frqwruqr gr pxqlfðslr gh Vær Mrær gr

Phulwl qr Ulr gh Mdqhlur uhfruwdgr gh dfrugr frp rv vhwruhv fhqvlwäulrv gr LEJH1

D Iljxud 516 prvwud r judir grv 686 vhwruhv fhqvlwäulrv gh Vdr Mrdr gr Phulwl

h{lvwhqwhv hp 4<<41 D pdwul} gh shvrv ì elqäuld h uhsuhvhqwd d dgmdfíqfld vlpsohv

gdv äuhdv1 Lvwr ì/ zlm @ 4 vh dv äuhdv l h m frpsduwlokdp iurqwhludv h ì ljxdo d 3/

fdvr frqwuäulr1

Page 29: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

57 FDSÐWXOR 51 DQÄOLVH GH GDGRV GH ÄUHD

Iljxud 515= Pdsd gr pxqlfðslr gh Vær Mrær gr Phulwl qr Ulr gh Mdqhlur glylglgr

hp vhxv vhwruhv fhqvlwäulrv gh�qlgrv shor LEJH1

Page 30: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

5161 PDSDV FRPR JUDIRV 58

coordenada x

coor

dena

da y

664000 666000 668000 6700007.47

6*10

^67.

478*

10^6

7.48

0*10

^67.

482*

10^6

12

34567 8

9 101112

13141516

1718

19

20

21

2223 242526 27 28293031

32

333435 3637 38

3940

41

42 4344 45 46

47 484950

5152

5354 5556 57

58

59

6061

6263 64 6566

6768

697071 72

73

7475

76777879 80

8182 8384 85 86 8788

899091 9293 94

959697

98

99

100101

102103

104 105

106

107108109 110 111

112113 114 115116

117118

119

120121 122123

124125

126 127128129

130131

132133134 135

136137138 139140

141

142143

144 145 146

147148

149150

151

152153154

155156 157 158

159

160161 162163 164165166167 168 169170

171 172173 174

175176177178 179180 181182183184

185186187188

189190191 192

193

194195196 197198 199200 201202 203204

205

206 207208 209210

211 212

213214 215

216217 218 219

220221222 223224225 226 227

228229

230

231232 233 234

235

236 237 238239 240 241242

243 244245246247

248249

250251 252253

254255256

257258259260 261 262263264265 266267268

269270

271272273

274275

276277

278279

280281282 283 284 285286 287

288289 290

291 292

293294 295

296 297298 299

300301302303

304 305306307

308 309310 311312313314 315

316 317318 319320321 322323 324 325326

327328 329

330331 332333334

335 336337338 339340 341342 343

344 345346 347348

349350 351

352

353

Grafo/Mapa de Sao Joao do Meriti

Iljxud 516= Judir gh yl}lqkdqfd grv vhwruhv fhqvlwäulrv gr pxqlfðslr gh Vær Mrær

gr Phulwl qr hvwdgr gr Ulr gh Mdqhlur1

Page 31: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

59 FDSÐWXOR 51 DQÄOLVH GH GDGRV GH ÄUHD

517 Dxwrfruuhodêær hvsdfldo

Vxsrqkd txh d hvwuxwxud hvsdfldo gdv q xqlgdghv jhrjuä�fdv ì gh�qlgd shod pdwul}

txdgudgd q�q gh shvrv Z rqgh zll @ 31 Vhmdp \4> \5> ===> \q yduläyhlv dohdwöuldv

phglgdv qdv q äuhdv1 D qrêær gh dxwrfruuhodêær hvsdfldo ghvwdv yduläyhlv hvwä

dvvrfldgd frp d lgìld gh txh ydoruhv revhuydgrv hp äuhdv jhrjuä�fdv dgmdfhqwhv

prvwudp0vh pdlv vlploduhv +rx pdlv glvvlploduhv, gr txh r hvshudgr vre d klsöwhvh

gh txh d glvwulexlêær gdv yduläyhlv ì lqyduldqwh sru shupxwdêær grv ðqglfhv 4> 5> ===> q

txh orfdol}dp dv äuhdv qr hvsdêr1 Ghvwh prgr/ d ghshqgíqfld hvsdfldo srgh rfruuhu

txdqgr äuhdv suö{lpdv whqghp d whu ydoruhv vlploduhv +dxwrfruuhodfdr srvlwlyd, rx

txdqgr äuhdv whqghp d whu ydoruhv glvvlploduhv +dxwrfruuhodfdr qhjdwlyd,1

R ðqglfh gh Prudq +4<83, phgh r judx gh fruuhodêær hqwuh sduhv gh yduläyhlv

\l dqg \m srqghudgr shod sur{lplgdgh jhjuä�fd phglgd sru zlm=

L @qS

l9@m zlm

�\l � \

�+\m � \ ,

V3S

l+\l � \ ,5

rqgh V3 ì d vrpdS

l 9@m zlm1 Txdqgr d pdwul} Z ì dshqdv d pdwul} elqäuld gh

dgmdfíqfld r ydoru gh V3 ì r qýphur gh sduhv gh äuhdv txh frpsduwlokdp iurqwhludv1

Qrwh txh L wrpd d irupd xvxdo gh xp frh�flhqwh gh fruuhodêær frp r qxphudgru

prvwudqgr d pìgld gh surgxwrv grv ghvylrv hp uhodêær d phgld joredo +srqghudgr

shod sur{lplgdgh jhrjuä�fd hqwuh dv äuhdv, h r ghqrplqdgru hqyroyh xpd phglgd

gh yduldelolgdgh grv ghvylrv1 Txdqgr dv yduläyhlv vdr hvsdfldophqwh lqghshqghqwhv/

r ydoru hvshudgr gh L ì suö{lpr gh }hur1 Txdqgr kä vlplodulgdgh hqwuh äuhdv

suö{lpdv/ L whqgh d vhu srvlwlyr hqtxdqwr txh vh äuhdv suö{lpdv whqghp d vhu

glvvploduhv +xp ihq÷phqr udur gh vhu revhuydgr,/ L whqgh d vhu qhjdwlyr1

Dvvxplqgr txh dv yduläyhlv dohdwöuldv vær l1l1g1*v frp glvwulexlêær qrupdo/ srgh

vhu prvwudgr +uhi BB, txh

H+L, @�4q� 4

Y du+L, @q5V4 � qV5 . 6V53

+q5 � 4,V53

�� �4q� 4

�5

Page 32: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

5171 DXWRFRUUHODÊÆR HVSDFLDO 5:

rqgh V4 h V5 vdr ixqêøhv gh zlm gh�qlgdv sru

V4 @4

5

[l 9@m

+zlm .zml,5

V5 @[l

+zl= .z=l,5 rqgh zl= @

[m

zlm h z=l @[m

zml

Dsduhqwhphqwh d h{suhvvær sdud Y du+L, qær ì R�q�4

�pdv lvwr qær ì yhugdgh

srlv wrgrv rv whuprv V3> V4 h VV5 wdpeìp ghshqghp gh q1 Gh idwr/ d glvwulexlêær

gh L ì dvvlqwrwlfdphqwh qrupdo vre frqglêøhv ud}rdoyhophqwh jhqìulfdv1 Vh dv

yduläyhlv dohdwöuldv vær l1l1g1*v frp glvwulexlêær qrupdo hqwærsqL frqyhujh sdud

xpd glvwulexlêær qrupdo d phglgd txh r qýphur q gh äuhdv dxphqwd vh/ h vö vh/

Sq

l@4 �m

l�Sq

l@4 �5l

�m@5 @ r+4, sdud wrgr m � 6

rqgh �4> ===> �q vær rv dxwrydoruhv gd pdwul}Z uhhvfdorqdgd sdud txh vxd vrpd V3

vhmd ljxdo d q1 Frqvlghudqgr dshqdv pdwul}hvZ vlpìwulfdv h wdpeìp uhhvfdorqdgd

frp V3 @ q/ Vhq +4<:9, prvwurx txh/ txdotxhu txh vhmd d glvwulexlêær frpxp

+srvvxlqgr vhjxqgr prphqwr �qlwr, gdv yduläyhlv \4> ===> \q/ vh pd{lzl= � f ?

4 h vh 3 ? olpq V4@q @ �5 ? 4/ hqwær d hvwdwðvwlfdsqL frqyhujh sdud xpd

glvwulexlêær Q+3> �5,1 Frp hvwhv uhvxowdgrv/ xp whvwh gh klsöwhvh gh txh qdr

h{lvwh ghshqghqfld hvsdfldo srgh vhu uhdol}dgr1 Edvwd sdgurql}du d hvwdwlvwlfd L h

frpsdudu frp rv ydoruhv gh xpd glvwulexlêær qrupdo sdguær1

Lqihol}phqwh/ hvwhv uhvxowdgrv vær gh xvr pxlwr olplwdgr sru gxdv ud}øhv1 D

sulphlud ud}ær ì d h{ljíqfld gh txh dv yduläyhlv srvvxdp d phvpd glvwulexlêær vre

K31 Txdqgr wudedokdprv frp wd{dv hslghplroöjlfdv rx sursruêøhv srsxodflrqdlv/

sru h{hpsor/ dv yduläyhlv whuær ydulåqfldv glihuhqwhv/ dv txdlv ghshqghp gd srs0

xodfær gh fdgd äuhd1 Txdqgr d glvwulexlêær gh \4> ===> \q qær iru d gh yduläyhlv

l1l1g1 d glvwulexlêær gd hvwdwðvwlfd L vre d klsöwhvh qxod qær ì dtxhod dsuhvhqwdgd

dflpd1 D vhjxqgd ud}ær ì edvhdgd qd vxsrvlêær ihlwd dflpd gh txh lqghshqgíqfld

hvsdfldo +d klsöwhvh qxod, ì htxlydohqwh d xpd glvwulexlêær frqmxqwd gh yduläyhlv

l1l1g*v txdqgr qd yhugdgh hod vxsøh dshqdv txh d glvwulexlêær frqmxqwd gh \4> ===> \3

q

Page 33: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

5; FDSÐWXOR 51 DQÄOLVH GH GDGRV GH ÄUHD

ì lqyduldqwh vre shupxwdêær grv ðqglfhv 4> ===> q1 Lvwr ì/ txh d glvwulexlêær frqmxqwd

ì shupxwäyho +h{fkdqjhdeoh/ hp lqjoív,1

Sdud d vhjxqgd remhêær/ dfhufd gd fruuhwd glvwulexlêær gdv yduläyhlv vre d

klsöwhvh qxod/ h{lvwh xpd vroxêær vre d irupd gh whvwhv gh dohdwrul}dêær frqgl0

flrqdgr qrv ydoruhv revhuydgrv gdv yduläyhlv1 Qhvwh fdvr/ �{dgrv rv ydoruhv revhu0

ydgrv/ fdofxod0vh r ydoru gh L vhohflrqdqgr0vh xp qýphur V ud}rdyhophqwh judqgh

gh shupxwdêøhv dohdwöuldv grv \4> ===> \3

q hqwuh dv äuhdv gd uhjlær1 R s0ydoru gh

xp whvwh gh vljql�fåqfld h{dwr ì gdgr sru n@+V . 4, rqgh n ì r srvwr gr ydoru

revhuydgr gh L ghqwuh rv V ydoruhv vlpxodgrv hoh suösulr1

Fol� h Rug +4<;4, prvwududp txh rv prphqwrv gh L vre shupxwdêær grv ðqglfhv

srgh vhu rewlgr whrulfdphqwh h txh d glvwulexlêær dvvlqwöwlfd gh L dlqgd hud qrupdo

vre ghwhuplqdgdv klsöwhvhv ehp jhudlv1 Hohv hqfrqwududp txh=

H+L, @�4q� 4

H+L5, @qi+q5 � 6q .6,V4 � qV5 . 6V5

3j � e5iq+q� 4,V4 � 5qV5 .9V53j

+q� 4,+q� 5,+q� 6,V53

rqgh

e5 @qS

+|l � |,7kS+|l � |,

5l5

Qr hqwdqwr/ hvwh pìwrgr gh dohdwrul}dêær qdr ì fdsd} vxshudu r vhjxqgr sure0

ohpd ghvfulwr dflpd/ r gd lq xíqfld gdv glihuhqwhv srsxodêøhv gdv äuhdv qd glv0

wulexlêær gh L= Sdud hvwh sureohpd/ Dvvxqêær h Uhlv +4<<<, iruqhfhudp xpd vroxêær

edvhdgd qxpd derugdjhp Ed|hvldqd hpsðulfd/ ghvfulwd qd suö{lpd vhêær1

Xp rxwur ðqglfh txh ì xvdgr frp phqru iuhtxíqfld gr txh r L gh Prudq ì r

ðqglfh sursrvwr sru Jhdu| +4<87, =

F @q� 4

5V3

qS

l 9@m zlm+\l � \m,5S

l+\l � \ ,5

rqgh V3 ì frpr dqwhv1 Qrwh txh hvwh ðqglfh ì vlplodu dr frqfhlwr gh ydulrjudpd

xwlol}dgr hp jhrhvwdwðvwlfd/ r qxphudgru vhqgr edvhdgr qd glihuhqfd txdguäwlfd

Page 34: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

5181 DXWRFRUUHODÊÆR HVSDFLDO FRP WD[DV 5<

pìgld hqwuh ydoruhv gh sduhv gh äuhdv srqghudgrv shod vxd vlplodulgdgh jhrj�ud�fd1

Hvwh ðqglfh qær ì pxlwr xwlol}dgr qd suäwlfd1

518 Dxwrfruuhodêær hvsdfldo frp wd{dv

Hp hvwxgrv hslghplroöjlfrv/ rv ydoruhv frqvlghudgrv qrv pdsdv xvxdophqwh vær

wd{dv rx ud}øhv +yhu fdsðwxor 6,1 Vh Ql ì r qýphur gh shvvrdv hp ulvfr h vh |l ì r

qýphur gh fdvrv rfruulgrv qd äuhd l/ d wd{d ì gh�qlgd frpr ul @ |l@Ql1 Txdqgr

dv srsxodêøhv hp ulvfr vær glihuhqwhv hqwuh dv äuhdv/ frpr ì gh sud{h/ hqwær dv

wd{dv srvvxhp ydulåqfldv glihuhqwhv h d klsöwhvh vxemdfhqwh dr whvwh edvhdgr qr

ðqglfh L gh Prudq gh txh dv yduläyhlv vær l1l1g1*v ì ylrodgd1 Phvpr qr whvwh gh

shupxwdêær/ d vxsrvlêær gh glvwulexlêær lqyduldqwh vre shupxwdêær ì ylrodgd srlv

qær ì yhugdgh txh dv äuhdv whqkdp d phvpd fkdqfh gh uhfhehu txdotxhu gdv wd{dv

revhuydgdv1 Äuhdv frp srsxodêøhv shtxhqdv srvvxhp wd{dv frp pdlru ydulåqfld

h pdlv surshqvdv d dvvxplu rv ydoruhv pdlv h{wuhprv ghqwuh rv revhuydgrv1

Zdowhu +4<<5, hvwxgd rv hihlwrv gh ylrodêøhv gh klsöwhvhv hp whvwhv gh dxwr0

fruuhodêær hvsdfldo1 Rghq +4<<8, h Zdogkùu +4<<9, id}hp gxdv sursrvwdv txh

surfxudp fruuljlu d glvwulexlêær gd hvwdwðvwlfd gr whvwh gh Prudq txdqgr rv gdgrv

vær wd{dv1 Dvvxqêær h Uhlv +4<<<, prvwududp txh hvwdv gxdv sursrvwdv srvvxhp

ghvydqwdjhqv h huurv txh dv wruqdp lqdsursuldgdv1 Doìp glvwr/ hvwhv dxwruhv sur0

sxvhudp xpd hvwdwðvwlfd gh whvwh txh vxshud dv gl�fxogdghv dsuhvhqwdgdv shodv

sursrvwdv dqwhulruhv/ frpr ghvfuhyhprv d vhjxlu1

Vhmdp �4> ===> �q dv wd{dv vxemdfhqwhv/ ghvfrqkhflgdv h srvvlyhophqwh glihuhqwhv/

gdv q äuhdv1 Vxsrqkd txh r qýphur gh fdvrv |l srvvxd glvwulexlêær gh Srlvvrq frp

hvshudqfd frqglflrqdo H+|lm�l, @ Ql�l +yhu r fdsðwxor 6 dfhufd ghvwd vxsrvlêær

vreuh d glvwulexlêær gdv frqwdjhqv,1 D wd{d hvwlpdgd ul @ |l@Ql srvvxl pìgld

frqglflrqdo H+ulm�l, @ �l h ydulåqfld Y du+ul$�l, @ �l@Ql1 Sruwdqwr/ dv wd{dv

hvwlpdgdv srvvxhp glihuhqwhv pìgldv h ydulåqfldv frqglflrqdlv1

Vxsrqkd txh dv wd{dv vxemdfhqwhv �4> ===> �q srvvxdp glvwulexlêær d sulrul l1l1g1

frp pìgld h ydulåqfld � h �/ uhvshfwlydphqwh1 Dvvlp/ d hvshudqfd pdujlqdo gh

ul ì � h d ydulåqfld pdujlqdo ì � . �@Ql1 Djrud/ dshqdv dv ydulåqfldv glihuhp

Page 35: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

63 FDSÐWXOR 51 DQÄOLVH GH GDGRV GH ÄUHD

hqwuh dv äuhdv/ vxdv pìgldv vhqgr ljxdlv/ h d ydulåqfld dxphqwd d phglgd txh d

srsxodêær ghfuhvfh1

Xvdqgr hvwlpdgruhv gh prphqwrv sursrvwrv sru Pduvkdoo +4<<4,/ qöv hqfrq0

wudprv e� @ v5 � e�@p h e� @S

|l@S

Ql rqgh p @S

Ql@q h v5 @S

Ql+ul�e�,5@SQl1 Sruwdqwr/ d hvshudqfd h ydulåqfld pdujlqdo gh ul vær hvwlpdgdv sru e�h yl @ e�. e�@Ql/ uhvshfwlydphqwh1 Vh yl ? 3/ qöv uhgh�qlprv yl @ e�@Ql1

Dr lqyìv gh xvdu dv wd{dv ul qr ðqglfh gh Prudq/ Dvvxqêær h Uhlv +4<<<,

sursøhv xvdu xp ghvylr hp uhodêær ã pìgld pdujlqdo hvwlpdgd sdgurql}dgd shod

hvwlpdwlyd gr ghvylr sdguær pdujlqdo hvwlpdgr=

}l @ul � e�s

yl

frp r ðqglfh ed|hvldqr hpsðulfr gh�qlgr hqwær frpr

HEL @qSZlm

SZlm}l}mS+}l � },

5

Frpr r ðqglfh L gh Prudq/ HEL whqgh d vhu srvlwlyr txdqgr h{lvwh dxwr0

fruuhodêær hvsdfldo1 R whvwh gh lqghshqgíqfld hvsdfldo frqwud d klsöwhvh qxod gh

dxvíqfld gh dxwrfruuhodêær hvsdfldo ì edvhdgr qd glvwulexllêær gh HEL vre shupx0

wdêær= shupxwh dohdwruldphqwh r yhwru }4> ===> }q hqwuh dv äuhdv xp judqgh qýphur

gh yh}hv1 Sdud fdgd pdsd shupxwdgr/ fdofxoh r ydoru gh HEL1 R s0ydoru ì gdgr

shod sursruêær gh yh}hv hp txh HEL shpxwdgr h{fhgh r HEL revhuydgr frp r

pdsd ruljlqdo1

Hvwh whvwh dsuhvhqwrx uhvxowdgrv pxlwr erqv pdqwhqgr r ydoru qrplqdo gr whvwh

vre d klsöwhvh qxod h srvvxlqgr xp srghu ehp vxshulru dr whvwh edvhdgr qr ðqglfh

L gh Prudq vre xpd judqgh ydulhgdgh gh klsöwhvhv dowhuqdwlydv1 Doìp glvwr/ r

whvwh dsuhvhqwrx sursulhgdghv gh urexvwh} iuhqwh d rxwolhuv txh qær h{lvwhp qrv

whvwhv dowhuqdwlyrv1

Page 36: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

Fdsðwxor 6

���������� �� �������

614 Lqwurgxêær

D dqäolvh gd glvshuvær hvsdfldo gr ulvfr gh xpd grhqêd ì ihlwd sulqflsdophqwh

dwudyìv gh pdsdv gh wd{dv gh lqflgíqfld1 Hvwhv pdsdv vær lqvwuxphqwrv ydolrvrv

sdud dsrqwdu dvvrfldêøhv hqwuh irqwhv srwhqfldlv gh frqwdplqdêær h äuhdv gh ulvfr

hohydgr/ sdud vxjhulu ghwhuplqdqwhv orfdlv gh grhqêdv h idwruhv hwlroörjlfrv gh0

vfrqkhflgrv h sdud ylvxdol}dêær gd glvwulexlêær hvsdfldo gd grhqêd1 Pdvrq +4<<8,

dsuhvhqwd rv yäulrv hvwxgrv gh fdpsr uhdol}dgrv frpr frqvhtxíqfld gdv txhvwøhv

oljdgdv drv ghwhuplqdqwhv dpelhqwdlv gr fåqfhu ohydqwdgdv dsöv dqäolvh grv gl0

yhuvrv dwodv hglwdgrv shor Qdwlrqdo Fdqfhu Lqvwlwxwh dphulfdqr1 Hvwhv hvwxgrv

deudqjhp fåqfhu rudo +Zlqq hw do1/ 4<;4,/ fdqfhu gr lqwhvwlqr +Slfnoh hw do1/ 4<;4,/

fåqfhu gh sxopær +]lhjohu hw do1/ 4<;7,/ fåqfhu gh eh{ljd +Krryhu dqg Vwudvvhu/

4<;3,1 Jodvv hw do1 +BB, surgx}ludp xp pdsd gh ulvfr gh grhqêd gh O|ph d sduwlu

gh gdgrv hslghplroöjlfrv h xp vlvwhpd gh lqirupdêær jhrjuä�fd1

D pdlru sduwh grv pdsdv vær frqvwlwxðgrv sru pdsdv whpäwlfrv rx frursoìwlfrv

rqgh xp frqmxqwr gh äuhdv vær vrpeuhdgdv gh dfrugr frp vhxv ydoruhv hp fhuwd

yduläyho gh lqwhuhvvh1 Sru h{hpsor/ d Iljxud 614 prvwud xp pdsd gd pruwdolgdgh

lqidqwlo qr hvwdgr gh Vær Sdxor qr dqr gh 4<<;1 R pdsd hvwä vxeglylglgr qrv

977 pxqlfðslrv h{lvwhqwhv hp 4<<; h fdgd pxqlfðslr uhfhehx xpd wrqdolgdgh gh

64

Page 37: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

65 FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

Iljxud 614= Pdsd gd wd{d gh pruwdolgdgh lqidqwlo qrv pxqlfðslrv gh Vær Sdxor qr

dqr gh 4<<;1

flq}d gh dfrugr frp r ydoru gr ðqglfh gh pruwdolgdgh lqidqwlo +PL,1 R ydoru gh PL

ì gh�qlgr frpr d ud}ær hqwuh r qýphur gh fuldqêdv dedl{r gh xp dqr gh lgdgh

pruwdv gxudqwh xp dqr h r qýphur gh fuldqêdv qdvflgdv ylydv qdtxhoh phvpr dqr

pxowlsolfdgr sru 43331

R pdsd iruqhfh xpd ghvfulêær gd glvwulexlêær gd PL qd uhjlær1 H{lvwh xp

judglhqwh gr Vxghvwh gr hvwdgr/ rqgh r ulvfr ì pdlv hohydgr/ sdud r Qrurhvwh/ rqgh

r uvlfr ghfolqd frqvlghudyhophqwh1 D lqwhqvlgdgh ghvwh ghfuìvflpr srgh wdpeìp

vhu dsuhfldgd frp xpd uäslgd frqvxowd ã ohjhqgd1 Ilfd hylghqwh d suhvhqfd gh

dxwrfruuhodêær hvsdfldo hqwuh dv wd{dv= pxqlfðslrv yl}lqkrv whqghp d whu wd{dv

pdlv vlploduhv gr txh grlv pxqlfðslrv hvfroklgrv dr dfdvr ghqwuh rv 977 h{lvwhqwhv1

Sru rxwur odgr/ r pdsd wdpeìp dsuhvhqwd fdudfwhuðvwlfdv txh uhyhodp dojxqv

grv vhxv sureohpdv1 Qrwd0vh d suhvhqêd gh dojxqv pxqlfðslrv frp ydoruhv pxlwr

glvfuhsdqwhv gh vhxv yl}lqkrv1 Qd yhugdgh/ dojxqv grv ydoruhv pdlv h{wuhprv gdv

wd{dv vær revhuydgrv qhvwhv fdvrv gh glvfuhsåqfld hvsdfldo1

Ioxwxdêøhv h{wuhpdv qdv wd{dv ohydp dojxpdv yh}hv ã ghflvær gh qær vh gl0

Page 38: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6151 PRGHOR FOÄVVLFR GH ULVFRV UHODWLYRV 66

yxojdu wd{dv dr qðyho gh pxqlfðslr rx txdqgr dv äuhdv vær pxlwr shtxhqdv1 Qr

hqwdqwr/ lvwr hqwud hp frq lwr frp xp grv sulqflsdlv remhwlyrv gh vh id}hu rv pd0

sdv1 Sdud dofdqêdu sohqdphqwh hvwhv remhwlyrv/ rv pdsdv ghyhp srvvxlu uhvroxêær

jhrjuä�fd dghtxdgd1 Lvwr lpsolfd txh d pdlru xwlolgdgh grv pdsdv rfruuh txdqgr

hohv xwlol}dp shtxhqdv uhjløhv jhrjuä�fdv frpr xqlgdghv gh dqäolvh1 Yäuldv ghvwdv

shtxhqdv äuhdv srvvxluær shtxhqdv srsxodêøhv gh ulvfr r txh dfduuhwduä wd{dv gh

lqflgíqfld frp pxlwd lqvwdelolgdgh1 Lvwr ì/ r dfuìvflpr rx ghfuìvflpr gh xp fdvr

qhvwdv äuhdv srghuä fdxvdu pxgdqêdv guävwlfdv qdv wd{dv1 Hp whuprv hvwdwðvwlfrv/

dv wd{dv gdv glyhuvdv äuhdv qær vær frpsduäyhlv mä txh srvvxhp ydulåqfldv pxlwr

glihuhqwhv1

Qhvwh fdsðwxor/ qrvvr remhwlyr ì dsuhvhqwdu rv sulqflsdlv pìwrgrv xvdgrv dwxdo0

phqwh sdud pdshdu wd{dv gh grhqêdv1 Rv pìwrgrv vær dsuhvhqwdgrv qr frqwh{wr

hslghplroöjlfr pdv hohv srghp vhu dgdswdgrv sdud pdsdv gh yduläyhlv vrfldlv rx

hfrq÷plfdv gh rxwurv wlsrv wdlv frpr wd{dv gh ghvhpsuhjr rx gh ixuwrv1 Ydprv

frqvlghudu lqfldophqwh r proghor foävvlfr gh ulvfrv uhodwlyrv h d dowhuqdwlyd vlpsohv

gh id}hu pdsdv gh wd{dv sdgurql}dgdv/ lqfoxlqgr d ghvfulêær gdv yäuldv irupdv

gh sdgurql}ä0odv1 D vhjxlu/ dsuhvhqwdprv gh irupd pdlv ghwdokdgd d hvwuxwxud

dohdwöruld gdv yduläyhlv revhuydgdv h grv sduåphwurv1 Ilqdophqwh/ frqvlghudprv d

vroxêær sursrvwd sru Fkr|qrzvnl +4<8<, h xp pìwrgr edvhdgr qxpd derugdjhp

ed|hvldqd hpsðulfd1

615 Prghor Foävvlfr gh Ulvfrv Uhodwlyrv

Rv gdgrv xvxdlv sdud hvwxgdu d yduldêær hvsdfldo gh ulvfrv ã vdýgh vær frqvwlwxðgrv

shodv frqwdjhqv gh hyhqwrv hp fdgd äuhd gh xp pdsd h gd srsxodêær hp ulvfr gh

vriuhu hvwhv hyhqwrv1 Dwxdophqwh/ h{lvwh xpd glvsrqlelolgdgh hqruph gh gdgrv sdud

txh lqwhuhvvdgrv idfdp hvwxgrv hslghplroöjlfrv1 R hqghuhfr kwws=22zzz1gdwdvxv1jry1eu/

sru h{hpsor/ glvsrqlelol}d pxlwrv gdgrv gh vdýgh jhruhihuhqfldgrv sru pxqlfð0

slrv rx äuhdv pdlruhv +hvwdgrv/ plfuruhjløhv/ uhjløhv/ hwf,1 Hqfrqwud0vh wdpeìp

glvsrqðyho qhvwh hqghuhfr r vriwzduh WDEZLQ txh shuplwh id}hu pdsdv ghvwdv

lqirupdêøhv1

Page 39: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

67 FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

R pdsd shuplwh id}hu frpsdudêøhv hqwuh dv äuhdv1 Ì fodur txh qær id} vhq0

wlgr id}hu pdsdv h frpsdudêøhv gdv frqwdjhqv euxwdv mä txh hodv ghshqghp gdv

srsxodêøhv gdv äuhdv1 Sdud shuplwlu frpsdudêøhv hqwuh glihuhqwhv srsxodêøhv qr

hvsdêr rx qr whpsr/ dv frqwdjhqv ghyhp vhu sdgurql}dgdv sdud jhudu wd{dv txh

wludp r hihlwr gdv glihuhqwhv srsxodêøhv1 R pdlv frpxp ì sdgurql}du dv frqwdjhqv

frqvlghudqgr dv glihuhqfdv hp wdpdqkr/ hvwuxwxud hwäuld h sru vh{r gdv srsxodêøhv

gh ulvfr gh fdgd äuhd1 D sdgurql}dêær srgh vhu wdpeìp sru äuhd/ sru whpsr gh

h{srvlêær rx rxwudv fdudfwhuðvwlfdv1

Ydprv frqvlghudu lqlfldophqwh dv glihuhqfdv gh wdpdqkr hqwuh dv srsxodfrhv

gdv äuhdv1 Frqvlghuh xppdsd sduwlflrqdgr hp q äuhdv lqgh{dgdv sru l> l @ 4> ===> q1

Vhmd |l d frqwdjhp gh hyhqwrv qd äuhd l qxp gdgr shuðrgr gh whpsr h Ql d vxd

srsxodêær hp ulvfr gh vriuhu r hyhqwr1 D wd{d shu fdslwd qd äuhd l ì gh�qlgd

frpr ul @ |l@Ql1 Ì frpxp xvdu wdpeìp ul @ +|l@Ql, 433333/ d wd{d sru 433

plo/ d txdo ì lqwhusuhwdgd frpr vhqgr r qýphur gh hyhqwrv txh vhuldp revhuydgrv

qd äuhd l fdvr hod wlyhvvh xpd srsxodêær wrwdo gh 433333 lqglyðgxrv1 Hvwd irupd

vlpsohv sdgurql}d dv frqwdjhqv srlv hodv djrud uhihuhp0vh d xpd phvpd srsxodêær

klsrwìwlfd gh wdpdqkr frqvwdqwh hp fdgd äuhd1

Vxsrqkd txh ghvhmd0vh id}hu frpsdudêøhv hqwuh grlv pdsdv gh xpd phvpd

uhjlær/ vhqgr rv pdsdv gh grhqêdv glihuhqwhv h srvvxlqgr lqflgíqfldv pxlwr glihu0

hqwhv1 Rx hqwær pdsdv uhihuhqwhv d xpd phvpd grhqêd pdv frp gdgrv gh shuðrgrv

gh whpsr pxlwr glvwdqwhv1 Sdud vlwxdêêøhv frpr hvwdv/ ì frpxp wudedokduprv frp

phglgdv gh ulvfr uhodwlydv dr qðyho pìglr qd uhjlær1 Hvwd phglgd ì d ud}ær +gh

pruwdolgdgh/ pruelgdgh/ hwf, sdgurql}dgd/ rx vwdqgdugl}hg +pruwdolw|/ pruelglw|/

hwf1, udwlr/ rx VPU/ hp lqjoív1 Hp fdgd äuhd l/ fdofxodprv r qýphur hvshudgr

Hl gh hyhqwrv fdvr r ulvfr qd äuhd l vhmd ljxdo dr ulvfr qd uhjlær wrwdo1 R ulvfr

wrwdo qd uhjlær ì gdgr shod wd{d +shu fdslwd, joredo u @S

l|l@S

lQl1 Dvvlp/

Hl @ uQl h d VPU ì rewlgd frpsdudqgr0vh r qýphur revhuydgr gh hyhqwrv hp l

frp r qýphur hvshudgr= VPUl @ |l@Hl1 Ghvwd irupd/ xp ydoru gh VPUl @ 4

lqglfd txh d äuhd l whyh wdqwrv fdvrv revhuydgrv txdqwr r txh vhuld hvshudgr fdvr

vhx ulvfr irvvh lgíqwlfr dr gd uhjlær wrgd1 Vh VPUl @ 5+3=8, hqwær d äuhd l whyh

xp qýphur gh fdvrv gxdv yh}hv pdlru +phqru, txh r hvshudgr vh vhx ulvfr irvvh

Page 40: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6151 PRGHOR FOÄVVLFR GH ULVFRV UHODWLYRV 68

lgíqwlfr dr gd uhjlær wrgd1 Ì frpxp whu d VPU pxowlsolfdgd sru 433 vhqgr hqwær

433 r qðyho gh uhihuíqfld gd äuhd joredo1

Sdud frphfdu d lqwurgx}lu r prghor hvwdwðvwlfr sdud pdsdv gh grhqêdv/ qöv

ydprv frqvlghudu r qýphur revhuydgr |l gh hyhqwrv qd äuhd l frpr xpd yduläyho

dohdwöuld1 D mxvwl�fdwlyd ì edvhdgd qr hqwhqglphqwr gh txh r ydoru uhdol}dgr qd

äuhd l srghuld vhu glihuhqwh fdvr r whpsr sxghvvh wudqvfruuhu qrydphqwh srlv yäulrv

hyhqwrv irudp iuxwrv gh ghflvøhv rx dêêøhv txh srghp vhu ylvwdv frpr dohdwöuldv1

R idwr ì txh vxsru dv yduläyhlv frpr dohdwöuldv lpsolfd txh |l srvvxl glvwulexlêær

gh suredelolgdgh/ ydoru hvshudgr/ ydulåqfld/ hwf1 D klsöwhvh pdlv frpxp txdqgr

rv hyhqwrv vær udurv +uhodwlydphqwh dr wdpdqkr gd srsxodêær, ì txh |l srvvxl

glvwulexlêær gh Srlvvrq frp ydoru hvshudgr �l hvshfð�fr sru äuhd1 Doìp gh iduwd

hylgíqfld hpsðulfd txh gä vxsruwh d hvwd klsöwhvh/ h{lvwhp wdpeìp uhvxowdgrv

whöulfrv sdud mxvwl�fä0od1 Xvdqgr klsöwhvh edvwdqwh uhdolvwdv h iudfdv/ Euloolqjhu

+4<;9, ghulyrx hvwd glvwulexlêær wudwdqgr dv wd{dv ylwdlv frpr hvwdwðvwlfdv rewlgdv d

sduwlu gh surfhvvrv gh Srlvvrq jhudqgr hyhqwrv qr gldjudpd gh Oh{lv/ xpd wìfqlfd

juä�fd eävlfd gh dqäolvh ghprjuä�fd1 Vh r ulvfr ì frqvwdqwh qd uhjlær/ hqwær

�l @ Hl @ uQl1

Txdqgr r ulvfr yduld frp d lgdgh rx r vh{r/ qær ì vx�flhqwh id}hu dshqdv d

sdgurql}dêær shor wdpdqkr gd srsxodêær1 D pdlruld grv ihq÷phqrv gh lqwhuhvvh

vhuær ghvwh wlsr wdlv frpr pruwhv ylrohqwdv/ txh dwlqjhp pdlv rv krphqv mryhqv/ d

pdlru sduwh grv fåqfhuhv h grhqêdv fdugðdfdv/ txh dwlqjhp rv pdlv yhokrv/ DLGV/

hwf1 Sdud wludu r hihlwr gdv glihuhqfdv gh glvwulexlfdr hwäuld h sru vh{r gdv srsx0

odfrhv +doìp gh vhx wdpdqkr,/ uhdol}dprv d sdgurql}dêær lqgluhwd1 Vhmd l r ðqglfh

gd äuhd h m r ðqglfh gd fodvvh gh lgdgh0vh{r1 Sru h{hpsor/ m @ 4 lqglfd pdvfxolqr

gh 3 d 7 dqrv gh lgdgh/ m @ 5 lqglfd pdvfxolqr gh 8 d < dqrv gh lgdgh/ hwf1

Ydprv �{du d dwhqêær lqlfldophqwh qxpd fodvvh m1 Sru h{hpsor/ m @ 8 txh

vljql�fd krphqv gh 53 d 57 dqrv gh lgdgh1 Vhmd |lm r qýphur gh hyhqwrv txh

rfruuhudp hqwuh shvvrdv gd fodvvh m qd äuhd l h Qlm r qýphur gh shvvrdv gd fodvvh

m qd äuhd l1 D wd{d joredo hp wrgr r pdsd uhihuhqwh dshqdv ã fodvvh gh lgdgh0vh{r

m ì gdgd sru um @S

l|lm@

SlQlm1 Hqwær Hlm @ umQlm ì r qýphur hvshudgr gh

hyhqwrv qd fodvvh m qd äuhd l vh r ulvfr qd fodvvh m irvvh frqvwdqwh qr hvsdêr1

Page 41: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

69 FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

R qýphur wrwdo gh hyhqwrv hvshudgr qd äuhd l vh r ulvfr gh fdgd fodvvh gh

lgdgh0vh{r ì frqvwdqwh qr hvsdêr ì gdgr sru Hl @S

m Hlm / d vrpd grv qýphurv

hvshudgrv qd äuhd l qdv glihuhqwhv fodvvhv gh lgdgh0vh{r1 D VPU ì hqwær fdofxodgd

frpr d ud}ær hqwuh r qýphur revhuydgr gh hyhqwrv h qýphur hvshudgr fdvr r ulvfr

irvvh frqvwdqwh qr hvsdfr= VPU @ |l@Hl1 Dvvlp/ qd klsöwhvh gh txh r ulvfr ì

frqvwdqwh qr hvsdêr hp fdgd fodvvh gh lgdgh0vh{r whprv |l �Srlvvrq+Hl, rqgh Hl

ì fdofxodgr frpr irl h{solfdgr dflpd1

Qd yhugdgh/ dr id}hu xp pdsd sdud hvwxgdu d yduldêær hvsdfldo/ mä hvwdprv

dvvxplqgr txh r ulvfr qær ì frqvwdqwh qr hvsdfr1 Hp jhudo/ d uhjlær gh hvwxgr

vhuäjudqgh r vx�flhqwh sdud txh r ulvfr qær vhmd frqvlghudgr frqvwdqwh1 Vlwxdêøhv

hp txh d klsöwhvh gh ulvfr frqvwdqwh ì gh lqwhuhvvh vær frpxqv qd vlwxdêær gh

whvwhv gh frqjorphudgrv rqgh dv uhjløhv gh hvwxgr vær shxtqhdv h krprjíqhdv1

Hvwh dvvxqwr vhuäwudwdgr hp rxwur fdsðwxor ghvwd eurfkxud1 Dvvlp/ r prghor

pdlv uhdolvwd ì dtxhoh hp txh rv ulvfrv uhodwlyrv yduldp qr hvsdfr1 Lvwr ì/ |l

srvvxl glvwulexlêær gh Srlvvrq frp ydoru hvshudgr �l @ �lHl1 R sduåphwur �l

txdqwl�fd d glihuhqfd gr ulvfr gd äuhd l uhodwlydphqwh ã pìgld gd uhjlær joredo rx

uhodwlydphqwh dr ydoru hvsdudgr Hl1

R hvwlpdgru gh pä{lpd yhurvvlplokdqêd e�l gr ulvfr uhodwlyr �l ì d VPU @

|l@Hl txh srvvxl ydulåqfld lqyhuvdphqwh sursruflrqdo dr qýphur hvshudgr gh hyhq0

wrv Hl1 Dvvlp/ txdqgr hvwh qýphur hvshudgr gh hyhqwrv iru shtxhqr/ d yduldelol0

gdgh gr hvwlpdgru gr ulvfr uhodwlyr srgh vhu pxlwr judqgh1 Hvwd vlwxdêær rfruuh

frp edvwdqwh iuhtxíqfld frp gdgrv hslghplroöjlfrv h ghprjuä�frv txdqgr dv

xqlgdghv hvsdfldlv gh dqäolvh vær pxqlfðslrv rx xqlgdghv dlqgd phqruhv1 Qhvwh

fdvr/ dv srsxodêøhv ghvwdv shtxhqdv äuhdv vhuær/ qd pdlruld grv fdvrv/ edvwdqwh

shtxhqd h ydl jhudu xp ydoru gh Hl edvwdqwh shtxhqr1 D frqvhtxíqfld ì txh rv

ydoruhv h{wuhprv gh e�l whqghp d rfruuhu qdv äuhdv frp shtxhqdv srsxodêøhv1 Lvwr

ì/ r txh pdlv fkdpd d dwhqêær qxp pdsd/ rv vhxv ydoruhv h{wuhprv/ ì r phqrv

suhflvdpdqwh hvwlpdgr1 Dv pdlruhv rvflodêøhv gr ulvfr uhodwlyr qær hvwduær/ hp

jhudo/ dvvrfldgdv frp yduldêøhv qr ulvfr vxemdfhqwh txh dv srsxodêøhv vriuhp pdv

vhuær dshqdv xwxdêær dohdwöuld fdvxdo1

Hvwh sureohpd dihwd wdpeìp xpd dqäolvh edvhdgd qdv wd{dv ul @ |l@Ql dr

Page 42: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6151 PRGHOR FOÄVVLFR GH ULVFRV UHODWLYRV 6:

lqyìv gr ulvfr uhodwlyr e�l 1 Dr wudedokduprv frp dv wd{dv vlpsohv/ dvvxplprv xp

prghor vlpsohv hp txh d sdgurql}dêær sru lgdgh h vh{r qær ì hihwxdgd h dvvlp |l

srvvxl glvwulexlêær frp ydoru hvshudgr �lQl rqgh �l ì d wd{d vxemdfhqwh gd äuhd

l hvwlpdgd sru ul1 Hod srvvxl ydulåqfld lqyhuvdphqwh sursruflrqdo dr wdpdqkr gd

srsxodêær Ql1 Dvvlp/ orfdlv frp shtxhqdv srsxodêøhv whuær judqgh yduldelolgdgh

hp vxdv wd{dv1 Xpd shtxhqd glihuhqfd qr qýphur gh fdvrv revhuydgr srghuäohydu

d judqgh yduldêøhv qrv ydoruhv gdv wd{dv1

H{dpsoh 4 Qxp duwljr foävvlfr h slrqhlur/ Fkr|qrzvnl +4<8<, frqvlghud d rfruu�hqfld

gh wxpruhv fhuheudlv hp frqgdgrv srorqhvhv1 Hoh dsrqwrx r sureohpd qrv vhjxlqwhv

whuprv= �Whqgr frqvwuxðgr xp pdsd txh prvwudyd dv wd{dv gh wxpruhv qr fìuh0

eur hp vhvvhqwd frqgdgrv +sryldw, gr vxo gd Sro÷qld/ 111 yhul�txhl txh dojxpdv

gdv wd{dv hudp pxlwr dowdv rx pxlwr edl{dv hp frpsdudêær frp d pìgld gd äuhd

wrwdo/ ljxdo d 814: sru 433 kdelwdqwhv1 Frpr hvvdv judqghv luuhjxodulgdghv jhrjuä0

�fdv hudp edvwdqwh vxusuhhqghqwhv/ hvwxghl rv gdgrv ghwlgdphqwh h qrwhl txh rv

frqgdgrv txh vh ghvyldydp +pxlwr gd pìgld, vhp txdotxhu h{solfdêær dsduhqwh

+wdlv frpr txdolgdgh gh fxlgdgr pìglfr/ glihuhqfdv qd frpsrvlfdr hwäuld/ hwf1,

wlqkdp srsxodêøhv shtxhqdv1 Frqvhtxhqwhphqwh/ phvpr xpd shtxhqd glihuhqfd

hp iuhtxíqfldv devroxwdv fuldyd xpd glihuhqfd vxevwdqfldo qdv wd{dv1 Lvwr ì/ rv

ghvylrv srghuldp pxlwr ehp vhu dwulexðgrv d yduldêøhv dprvwudlv1�

Frqvlghudqgr rv gdgrv/ qrwdprv txh d pdlru wd{d/ fruuhvsrqghqwh dr frqgdgr

gh Ohvnr/ hvwädvvrfldgd �d phqru srsxodêær +4:1333 kdelwdqwhv,1 D rfruuíqfld

gh grlv fdvrv qhvvh frqgdgr ì uhsrqväyho shod wd{d gh 44/:: sru 433 plo1 Fdvr

wlyhvvh rfruulgr dshqdv xp fdvr/ hvvd wd{d edl{duld sdud 8/< sru 433 plo/ xp ydoru

frqvlvwhqwh frp dv wd{dv grv rxwurv frqgdgrv1 Sru rxwur odgr/ d rfruu�hqfld gh

wuív fdvrv iduld d wd{d sxodu sdud 4:/: sru 433 plo1

Hvvh hihlwr guävwlfr txh d dglêær rx vxewudêær gh xp rx srxfrv fdvrv dfduuhwd

qd wd{d qær vh yhul�fd qdtxhohv frqgdgrv frp judqghv srsxodêøhv1 Sru h{hpsor/

frqvlghuh Jruolfh txh srvvxl d vhjxqgd pdlru wd{d/ ljxdo d 43/; sru 433 plo1 Vh

xp fdvr ì vxewudðgr rx dglflrqdgr/ d wd{d pxgd sdud </9 rx 45/3 sru 433 plo/

uhvshfwlydphqwh1 Srsxodêøhv prghudgdv whuldp hihlwr lqwhuphgläulr frpr/ sru h{0

Page 43: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6; FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

hpsor/ Su}hzruvn txh whuld wd{dv ljxdlv d 4/; h 8/6 qr fdvr gd vxewudêær rx dglêær

gh xp fdvr dglflrqdo1

Ì lpsruwdqwh hqidwl}du txh d fdudfwhul}dêær gr txh frqvwlwxl xpd srsxodêær

judqgh rx shtxhqd ghshqgh gr ulvfr vxemdfhqwh1 Xpd phvpd srsxodêær srgh vhu

frqvlghudgd shtxhqd sdud fdofxodu xpd wd{d dvvrfldgd frp xp ulvfr pxlwr edl{r

h frqvlghudgd judqgh sdud xp ulvfr pdlv frpxp1 Vxsrqkd/ sru h{hpsor/ txh r

lqwhuhvvh uhvlgh qd ud}ær gh vh{rv rx/ htxlydohqwhphqwh/ qd sursruêær gh shvvrdv

gr vh{r pdvfxolqr qxpd srsxodêær1 Xpd shvvrd hvfroklgd dr dfdvr srvvxl xpd

fkdqfh +�ulvfr�, dsur{lpdgdphqwh ljxdo d 3/8 gh vhu krphp1 Xpd wd{d ljxdo

ã sursruêær gh krphqv qd srsxodêær ydl yduldu pxlwr srxfr vh r wdpdqkr gd

srsxodêær iru 833 rx pdlv1 Qr hqwdqwr/ hvvd srsxodêær gh 833 ì fodudphqwh

lqdghtxdgd sdud fdofxodu d wd{d gh pruwdolgdgh sru fåqfhu gh sxopær/ ghylgr ã

judqgh yduldelolgdgh gd wd{d uhvxowdqwh1

R sureohpd sruwdqwr ì txh d yduldêær gdv wd{dv ì pxlwr judqgh txdqgr d

srsxodêær ì shtxhqd sdud r ulvfr txh hvwä vre frqvlghudêær1 Hvvh sureohpd hvwä

suhvhqwh qr gh pruwdolgdgh lqidqwlo hp Plqdv Jhudlv dsuhvhqwdgr d vhjxlu1

H{dpsoh 5 D Iljxud 615 prvwud dv wd{dv gh pruwdolgdgh lqidqwlo +sru 4333, hp

pxqlfðslrv gh Plqdv Jhudlv hp 4<<71 D pruwdolgdgh lqidqwlo ì xpd wd{d fxmr

qxphudgru ì r qýphur txh pruuhudp frp phqrv gh xp dqr gh lgdgh qxp fhuwr

shuðrgr glylglgr shor qýphur gh fuldqêdv qdvflgdv ylydv qr phvpr shuðrgr1 Hp

PJ/ hqfrqwudprv xpd wd{d joredo gh 641; sru 43331 Qr juä�fr/ r hl{r krul}rqwdo

ì r orjdulwpr gr qýphur gh qdvflgrv ylyrv h fdgd srqwr uhsuhvhqwd xp pxqlfð0

slr1 Revhuyd0vh d qðwlgd irupd gh xp ixqlo frp d yduldfår gdv wd{dv vhqgr pxlwr

pdlru qrv pxqlfðslrv phqruhv1 Hperud sduwh ghvwd yduldfår srvvd hvwdu dvvrfl0

dgd frp ulvfrv pxlwr glihuhqwhv hp pxqlfðslrv shtxhqrv/ qhqkxp hslghplroöjr

dfuhglwduld hp wd{dv qhvwh shuðrgr wær dowdv txdqwr 533 pruwhv d fdgd 43331 D

hqruph yduldêær gdv wd{dv txdqgr r qýphur gh qdvflgrv ylyrv ì shtxhqr ì ghylgr

d sxud xwxdêær dohdwöuld1 Sdud vh frqyhqfhu glvwr/ frqvlghuh rv 48 pxqlfðslrv

txh wlyhudp 3 pruwhv h phqrv txh 63 qdvflgrv ylyrv1 Vh xpd ýqlfd pruwh wlyhvvh

vlgr uhjlvwudgd qhvwhv pxqlfðslrv/ dv wd{dv sdvvduldp gh 3 +r phqru ydoru srvvðyho,

Page 44: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6151 PRGHOR FOÄVVLFR GH ULVFRV UHODWLYRV 6<

logaritmo do numero de nascidos vivos

taxa

de

mor

talid

ade

infa

ntil

(por

100

0)

4 6 8 10

050

100

150

200

Iljxud 615= Wd{d gh pruwdolgdgh lqidqwlo +sru 4333, yhuvxv r orjdulwpr gr qýphur

gh qdvflgrv ylyrv hp pxqlfðslrv plqhlurv hp 4<<71 Fdgd srqwr uhsuhvhqwd xp

pxqlfðslr1

sdud ydoruhv hqwuh 6: h 96/ wrgrv/ h{fhwr xp/ dflpd gr whufhlur txduwlo1

Sdud vroxflrqdu hvwh sureohpd/ dojxpdv rsêøhv srghp vhu frqvlghudgdv1 D

sulphlud ì djuhjdu äuhdv sdud irupdu äuhdv pdlruhv sdud dqäolvh1 D ghvydqwdjhp

glvwr ì shughu d lqirupdêær orfdol}dgd1 Rxwud rsêær irl vxjhulgd sru Fkr|qrzvnl

+4<8<, h ì edvhdgd hp pdsdv gh suredelolgdghv/ frpr ghvfuhyhprv qd suö{lpd

vhêær1 Hvwd vroxfær yhp fdlqgr hp ghvxvr srlv dsuhvhqwd fhuwdv lqfryhqlíqfldv h

srutxh yhp vhqgr vxshudgd sru rxwudv vroxêøhv1 R uhvwdqwh gr fdsðwxor ì ghglfdgr

d xpd hvwudwìjld phokru/ d gh surfxudu hvwlpdu phokru ulvfr orfdol}dgr gh fdgd

äuhd1 Srgh0vh rewhu judqgh uhgxêær gr sureohpd gd yduldelolgdgh gh shtxhqdv

äuhdv xwlol}dqgr derugdjhqv ed|hvldqdv1

Page 45: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

73 FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

616 Pdsdv gh suredelolgdghv

Sdud hylwdu r sureohpd gd judqggh yduldelolgdgh gh wd{dv edvhdgdv hp shtxhqdv

srsxodêøhv shtxhqdv/ Fkr|qrzvnl +4<8<, sursøh id}hu pdsdv vxevwlwxlqgr dv wd{dv

sru suredelolgdghv vlploduhv dr S0ydoru gh xp whvwh1 Xp pdsd whpäwlfr edvhdgr

qhvvd sursrvwd ì fkdpdgr gh pdsd gh suredelolgdgh1 Dr lqyìv gh pdshdu d wd{d/

id}0vh xp pdsd gd suredelolgdgh gh rewhu xpd frqwdjhp txh ì pdlv h{wuhpd txh

dtxhod gh idwr revhuydgd/ vre d klsöwhvh gh txh r ulvfr ì frqvwdqwh qd uhjlær1

Vxsrqkd txh r qýphur revhuydgr gh fdvrv |l srvvxl glvwulexlêær gh Srlvvrq

frp ydoru hvshudgr Hl vljql�fdqgr xp ulvfr frqvwdqwh qr hvsdêr hp fdgd fodvvh

gh lgdgh0vh{r1 Vhmd [ xpd yduläyho frp d phvpd glvwulexlêær txh |l1 Lvwr ì/

[ �Srlvvrq+Hl,1 Gh�qd hqwær=

�l @

;?= S +[ � |l, vh |l � Hl

S +[ � |l, vh |l ? Hl

<@>Dvvlp/ xp ydoru gh �l pxlwr suö{lpr gh }hur lqglfd txh d wd{d ì pxlwr dowd

rx pxlwr edl{d +uhodwlydphqwh dr ydoru hvshudgr,1 D ydqwdjhp ghvwh pìwrgr ì

txh hoh vxevwlwxl d wd{d sru xpd phglgd txh ohyd hp frqwd d qdwxuh}d hvwrfävwlfd

gd frqwdjhp |l frqvlghudqgr vxd yduldelolgdgh1 Ghvwh prgr/ hoh hylwd dwulexlu

vljql�fdgr d wd{dv pxlwr h{wuhpdv pdv edvhdgdv hp shtxhqrv h{fhvvrv dohdwöulrv

fdvxdlv hp shtxhqdv srsxodêøhv h txh vær frpsdwðyhlv frp d klsöwhvh gh txh r

ulvfr qdtxhod äuhd ì ljxdo dr hvshudgr vre d klsöwhvh gh ulvfr frqvwdqwh qr hvsdfr1

Hqwuhwdqwr/ hvwd phglgd vriuh gr sureohpd frqwuäulr1 Vhxv ydoruhv vhuær pxlwr

suö{lprv gh }hur fdvr d srsxodêær vhmd pxlwr judqgh1 Gh idwr/gr phvpr prgr txh

xp s0ydoru/ �l ì lq xhqfldgr shor wdpdqkr gd srsxodêær gh ulvfr frp shtxhqdv

glihuhqêdv hqwuh |l h Hl ohydqgr d �l � 3 vh Hl ì judqgh1 Sru h{hpsor/ frp

Hl @ 4333/ vh |l A 4385 hqwær �l ? 3=381 Qr hqwdqwr/ d glihuhqfd hqwuh hvvhv

ydoruhv ì gh dshqdv 8=5( gr ydoru hvshudgr1 Gh irupd xp srxfr pdlv jhudo/

vxsrqkd txh |l �Hl @ 4=38Hl1 Xvdqgr r Whruhpd Fhqwudo gr Olplwh/ whprv

�l @ S +[ � |l, @ S

�[ �Hls

Hl

A|l �Hls

Hl

�� S

�Q+3> 4, A

4=38HlsHl

��$ 3

txdqgr Hl �$ 31

Page 46: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6161 PDSDV GH SUREDELOLGDGHV 74

Hperud d lgìld grv pdsdv gh suredelolgdghv vhmd shuplwlu frpsdudêøhv sru

phlr gd sdgurql}dêær gdv wd{dv hp xpd hvfdod gh suredelolgdgh/ lvwr qær ì srvvðyho

vh dojxpdv srsxodêøhv gh ulvfr vær judqghv srlv hqwær whuhprv ydoruhv h{wuhprv

gd suredelolgdgh frpr frqvhtxíqfld gr srghu gr whvwh sdud ghwhfwdu shtxhqrv

didvwdphqwrv gdv klsöwhvhv ihlwdv sdud r fäofxor gdv suredelolgdghv �l1

Qr hqwdqwr/ d sulqflsdo ghvydqwdjhp ghvwh pìwrgr ì vxsru txh dv wd{dv gh

fdgd orfdo ghyhuldp vhu ljxdlv d xpd wd{d joredo frqvwdqwh hp wrgr r pdsd1 Lvwr

hvwä lpsoðflwr qr fäofxor grv �l*v txdqgr dvvxph0vh txh d glvwulexlêær gh [ srvvxl

pìgld Hl1 Lvwr qær vhuä ud}räyho qxp pdsd gh xpd äuhd h{whqvd rx frp judqgh

yduldêær qr ulvfr wdlv frpr pdsdv gh hvwdgrv eudvlohlurv glylglgrv hp pxqlfðslrv

rx phpvr pdsdv gh phwuösrohv glylygdv hp edluurv1

Xp lpsruwdqwh sureohpd dglflrqdo ì txh hohv ljqrudp r ydoru gd wd{d gh prgr

txh/ qxppdsd/ gxdv äuhdv frp d phvpd VPU srghp whu �l*v pxlwr glihuhqwhv h dv

äuhdv pdlv h{wuhpdv srghp vhu vlpsohvphqwh dtxhodv frp dv pdlruhv srsxodêøhv1

Rxwud ghvydqwdjhp ghvvhv pdsdv gh suredelolgdgh ì txh hohv qær ohydp hp

frqwd dv hvshudgdv vlplodulgdghv hqwuh äuhdv frqwðjxdv1 Hvwdv vlplodulgdghv vær

ghylgr d xvxdo yduldêær vxdyh gr ulvfr vreuh äuhd vhqgr pdshdgd1 Lqfrusrudu

hvwd lqirupdêær qdv hvwlpdwlydv gh ulvfr srgh ohydu d pdsdv frp phqrv xwxdêær

dohdwöuld h dvvlp d xpd glihuhqfldêær pdlv suhflvd hqwuh r txh ì gh idwr ulvfr

hohydgr h r txh ì xwxdêær dohdwöuld fdxvdgd sru shtxhqdv srsxodêøhv rx judqgh

srwíqfld gh ghwhfwdu glihuhqêdv vxevwdqwlydphqwh ghvsuh}ðyhlv1

R phokru ì qær id}hu rv pdsdv gh suredelolgdghv edvhdgrv qdv phglgdv �l1

Qr hqwdqwr/ hvwdv phglgdv vær idflophqwh fdofxoäyhlv1 Dvvlp/ sdud dphql}du hvwdv

ghvydqwdjhqv h dlqgd xvdu dv phglgdv �l/ srgh0vh surfhghu hp gxdv hwdsdv dr id}hu

pdsdv gh hvwlpdwlydv gh ulvfrv uhodwlyrv rx wd{dv1 Sulphludphqwh/ frqvlghudqgr0

vh dshqdv r frqkhflphqwr gr sureohpd h grv ydoruhv wðslfrv rx wrohuäyhlv gh xpd

grhqêd/ uhvsrqgh0vh ã txhvwær= D wd{d ul +rx VPUl, ì pxlwr dowd2edl{d rx srgh

vhu frqvlghudgd wðslfd rx dfhlwäyho B Vh iru wðslfd/ qdgd d id}hu1 Vh dowd +rx edl{d,/

uhvsrqgh0vh= R ydoru �l ì suö{lpr gh 3B Vh d uhvsrvwd iru qær/ qdgd d id}hu1 Vh

iru vlp/ hqwær hvwd wd{d ul ì dowd +rx edl{d, h srvvxl shtxhqd ydulåqfld srghqvr

vhu frqvlghudgd xpd äuhd gh ulvfr hohydgr +rx pdlv edl{r txh r wðslfr gd grhqêd,1

Page 47: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

75 FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

taxa de mortalidade infantil em MG

prob

abili

dade

rho

_i

0 50 100 150 200

0.0

0.1

0.2

0.3

0.4

0.5

rho_i = 0.05

taxa > 50

Iljxud 616= Juä�fr gdv wd{dv yhuvxv d suredelolgdgh �l sdud rv gdgrv gh pruwdol0

gdgh lqidqwlo gh Plqdv Jhudlv1

H{dpsoh 6 Sdud xwlol}du hvwh surfhglphqwr gh gxdv hwdsdv qr h{hpsor gd pru0

wdolgdgh lqidqwlo hp Plqdv Jhudlv/ frqvlghuh r juä�fr gd Iljxud 616 txh prvwud d

wd{d gh pruwdolgdgh qr hl{r krul}rqwdo h d suredelolgdgh �l qr hl{r yhuwlfdo1 Ydo0

ruhv gh pruwdolgdgh lqidqwlo pdlruhv txh 83 sru plo vhuldp prwlyr gh suhrfxsdêær/

gr srqwr gh ylvwd gd vdýgh sýeolfd1 Pxqlfðslrv frp hvwhv ydoruhv vær dtxhohv d

gluhlwd gd olqkd yhuwlfdo1 Sru rxwur odgr/ dshqdv pxqlfðslrv frp �l shtxhqrv/

gljdprv dedl{r gh 3138/ ghyhuldp vhu prwlyr gh suhrfxsdêær h hvwhv vær dtxhohv

dedl{r gd olqkd krul}rqwdo1 Yhprv txh txdvh wrgrv rv ydoruhv gh wd{dv pxlwr hoh0

ydgdv frqwlqxdp dsduhfhp dedl{r gd olqkd �l ? 3=381 Qr hqwqdwr/ yhuhpvr pdlv

wdugh frp rv pìwrgrv ed|hvldqrv txh hvwh txdgur qær shupdqhfh dvvlp1 Frpr

glvvhprv dqwhv/ xp grv sulqflsdlv ghihlwrv gd phwrgrorjld edvhdgd qrv �l ì vxsru

xp ulvfr frqvwdqwh qr hvsdfr r txh qær ì yhugdgh qr fdvr gh pruwdolgdgh lqidqwlo

hp PJ1

Page 48: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6171 HVWLPDÊÆR ED\HVLDQD HPSÐULFD 76

Sdud vxshudu hvwdv gl�fxogdghv/ pìwrgrv Ed|hvldqrv hpsðulfrv rx lqwhludphqwh

Ed|hvldqrv wíp vlgr sursrvwrv qd olwhudwxud1 Hvwhv pìwrgrv/ dr hvwlpdu r ulvfr gh

xpd shtxhqd äuhd/ wíp frpr lgìld fhqwudo r xvr gh lqirupdêær gdv rxwudv äuhdv

txh frpsøhp d uhjlær gh hvwxgr1 Ghvwh prgr/ glplqxl0vh r huur txdguäwlfr pìglr

wrwdo gd hvwlpdêær grv ulvfrv1 R pìwrgr ed|hvldqr hpsðulfr ì dsuhvhqwdgr qhvwh

fdsðwxor hqtxdqwr txh r pìwrgr lqwhludphqwh ed|hvldqr ì dsuhvqhwdgr qr suö{lpr

fdsðwxor1 Dwxdophqwh/ r pìwrgr lqwhludphqwh ed|hvldqr ì suhihuðyho sru ohydu hp

frqwd wrgd d yduldelolgdgh suhvhqwh qrv gdgrv h sru shuplwlu lqihuíqfldv pxlwr

pdlv ulfdv hp prghorv pdlv vr�vwlfdgrv1

617 Hvwlpdêær ed|hvldqd hpsðulfd

61714 Ed|hv Hpsðulfr h r Sdudgr{r gh Vwhlq

Xp grv uhvxowdgrv pdlv suryrfdqwhv gh whruld hvwdwðvwlfd qdv ýowlpdv gìfdgdv ì

r ihq÷phqr fkdpdgr sdudgr{r gh Vwhlq rx hvwlpdgruhv gh Mdphv0Vwhlq rx dlqgd

hvwlpdgruhv gh frqwudêær +vkulqndjh hvwlpdwruv,1 Qd vxd irupd pdlv vlpsohv/ d

vlwxdêær ì d vhjxlqwh= xpd frohêær gh phglêøhv lqghshqghqwhv [4> = = = >[n ì ihlwd

h [l � Q+�l> 4, rqgh rv �l*v vær frqvwdqwhv ghvfrqkhflgdv h �{dv1 Rv sduåphwurv

�4> = = = > �n qær suhflvdp vhu uhodflrqdgrv/ srghqgr uhihulu0vh d sureohpdv frpsoh0

wdphqwh glvwlqwrv frpr/ sru h{hpsor/ r suhêr pìglr gr txlor gh ihlmær hp Ehor

Krul}rqwh h d dowxud pìgld grv mdsrqhvhv dgxowrv txh ylyhp hp N|rwr1 Ghvhmd0vh

hvwlpdu rv �l*v vlpxowdqhdphqwh frp d ixqêær gh shugd frpsrvwd

O+�> a�, @

n[l@4

+�l � a�l,5

zkhuh a�3

@ + a�4> = = = > a�n, h � @ +�4> = = = > �n,1 R ghvhpshqkr gr hvwlpdgru a� ì phglgr

shod ixqêær gh ulvfr

U+�> a�, @ HO+�> a�,=

Page 49: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

77 FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

zkhuh a�3

@ + a�4> = = = > a�n, h � @ +�4> = = = > �n,1 R ghvhpshqkr gr hvwlpdgru a� ì phglgr

shod ixqê�ær gh ulvfr

U+�> a�, @ HO+�> a�,=

D ghvfrehuwd gh Vwhlq+4<89,/ uh�qdgd hp Mdphv h Vwhlq +4<94,/ ì txh/ vh n � 6/

pìgldv srqghudgdv grv [l*v v�ær hvwlpdgruhv phokruhv grv �l*v gr txh r hvwlpdgru

öeylr a�rl @ [l1 Hirq h Pruulv +4<:6, prvwududp txh hvwhv hvwlpdgruhv srgldp

vhu ylvwrv frpr hvwlpdgruhv ed|hvldqrv hpsðulfrv prwlydqgr hqwær xpd vìulh gh

wudedokrv xwlol}dqgr hvwd phwrgrorjld1 Xpd frqmxqwr ghvvhv wudedokrv dsduhfhx

qd äuhd gh pdshdphqwr gh grhqêdv/ frpr ghvfuhyhprv d vhjxlu1

61715 Wd{dv h ulvfrv uhodwlyrv frpr yduläyhlv dohdwöuldv

Frqvlghuh xpd uhjlær sduwlflrqdgd hp q äuhdv lqgh{dgdv sru l> l @ 4> = = = > q1

Vxsrqkd txh d wd{d dqxdo gh hyhqwrv +ghvfrqkhflgd, hp fdgd äuhd ì ghqrwdgd

sru �l h txh ul @ |l@Ql ì d wd{d revhuydgd/ rqgh |l ì r qýphur gh hyhqwrv qd äuhd

l h Ql ì r qýphur gh shvvrdv hp ulvfr1 Ì frpxp vxsru txh/ gdgd d wd{d ghvfrq0

khflgd �l/ d frqwdjhp |l gr qýphur gh fdvrv srvvxl glvwulexlê�dr gh suredelolgdgh

gh Srlvvrq frp hvshudqêd frqglflrqdo H+|lm�l, @ ql �l h ydulåqfld frqglflrqdo

Ydu+|lm�l, @ ql �l1 Qxp frqwh{wr qær0ed|hvldqr/ txdqgr |l srvvxl glvwulexlê�ær

Srlvvrq rx elqrpldo/ d wd{d ul ì d phokru hvwlpdwlyd gh �l qr vhqwlgr gh plqlpl}du

r huur pìglr gh hvwlpdêær H+�l � a�l,51

Sduhfh ud}räyho vxsru txh dv glihuhqêdv hqwuh dv wd{dv ghvfrqkhflgdv �l srvvxhp

xpd uhjxodulgdgh rx krprjhqhlgdgh ghulydgd grv surfhvvrv vrfldlv h dpelhqwdlv

vxemdfhqwhv txh dihwdp d uhjlær hp hvwxgr1 Hvvd uhjxodulgdgh qrv shuplwh prghodu

dv yduldêøhv qrv �l dwudyìv gh xpd glvwulexlêær gh suredelolgdgh1 Hvwh prghor

sdud dv wd{dv ghvfrqkhflgdv �l uhfrqkhfh txh hodv q�ær vær q�ýphurv wrwdophqwh

duelwuäulrv/ frpsohwdphqwh ghvfrqhfwdgrv/ pdv txh jxdugdp fhuwd uhodêær hqwuh

vl1 Sru h{hpsor/ sdud xp gdgr ihq÷phqr qxpd uhjlær/ dv wd{dv gh fdgd vxe0äuhd

surydyhophqwh yær hvwdu frqfhqwudgdv qxpd idl{d gh ydoruhv frp dojxqv srxfrv

ydoruhv srvvlyhophqwh pdlv didvwdgrv1

Xpd derugdjhp ed|hvldqd ì d pdlv dghtxdgd h h{ðyho sdud lqfrusrudu hvwd

Page 50: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6171 HVWLPDÊÆR ED\HVLDQD HPSÐULFD 78

lgìld lqwxlwlydphqwh vlpsohv h idflophqwh dfhlwäyho1 Hvwd derugdjhp/ qd vxd yhu0

vær rulhqwdgd sdud dqäolvh gh gdgrv/ dvvxph txh qrvvr frqkhflphqwr rx idowd gh

frqkhflphqwr +lqfhuwh}d, dfhufd gdv wd{dv �{dv h ghvfrqkhflgdv �l> l @ 4> = = = > q/

srgh vhu uhsuhvhqwdgr sru xpd glvwulexlêær gh suredelolgdgh1 Pdlv hvshfl�fd0

phqwh/ rv ydoruhv ghvfrqkhflgrv h �{r vhuldp uhdol}dêøhv gh yduläyhlv dohdwöuldv

�l> l @ 4> ===> q frp fhuwd glvwulexlêær frqmxqwd1 R remhwlyr ì dwxdol}du qrvvr frq0

khflphqwr dfhufd ghvwdv txdqwlgdghv ghvfrqkhflgdv dsöv revhuydu rv gdgrv1 Ì

frpxp xvdu xpd qrwdêær xp srxfr pdlv dpeðjxd ghqrwdqgr dpedv/ wdqwr �l

txdqwr �l/ sru xp ýqlfr vðperor/ txh vhuä �l qhvwh olyur1

R fdvr pdlv vlpsohv vxsøh txh �l> l @ 4> = = = > q vær lqghshqghqwhv h srvvxhp

xpd glvwulexlêær gh suredelolgdgh frpxp frp ydoru hvshudgr �� h ydul�åqfld �5�1

Ì ýwlo lpdjlqdu fdgd äuhd l hvfrokhqgr vxd wd{d �l gh irupd dohdwöuld d sduwlu gh

xpd glvwulexlêær frpxp1 Ghvvh prgr/ srgh0vh lqwhusuhwdu �� frpr vhqgr r ydoru

hvshudgr gd wd{d gh xpd äuhd hvfroklgd dr dfdvr qd uhjlær1 D glvwulexlêær frpxp

gdv wd{dv srghuld vhu edvwdqwh frpsolfdgd frp yäuldv prgdv h vhp xpd h{suhvvær

pdwhpä wlfd frqkhflgd1

Qr hqwdqwr/ qd suäwlfd/ hvfrokh0vh xpd glvwulexlêær vlpsohv1 Sru h{hpsor/ dv

wd{dv �l srghuldp hvwdu vhqgr jhudgdv d sduwlu gh xpd glvwulexlêær jdpd frp

sdu�åphwurv � h �/ ghqrwdgd sru �+�> �,1 D �jxud 617 prvwud d ghqvlgdgh gh

suredelolgdgh gh xpd jdppd frp sduåphwurv � @ 5 h � @ 431 D glvwuexlêær

jdpd �+�> �, srvvxl ydoru hvshudgr �� @ �@� h ydul�åqfld �5� @ �@�51 Sdud r

h{hpsor gd �jxud 617/ whprv �� @ 3=5 h �5� @ 3=35 rx �� @ 3=471

Qr fdvr grv gdgrv gh Plqdv Jhudlv/ revhuydprv wd{dv h{wuhpdv gh 53 sru plo

rx 3151 Hvwd vær wd{dv lqdfhlwdyhophqwh dowdv h gl�fophqwh yhurvvðplvvhlv qr txdgur

gh vdýgh sýeolfd eudvlohlud qrv whpsrv dwxdlv1 Xpd pruwdolgdgh lqidqwlo gh 5(

rx suö{lpd glvvr vhuld xpd yhugdghlud fdodplgdgh sýeolfd1 Frpr d glvwulexlêær

dflpd dwulexl pdvvd gh suredelolgdgh ljxdo d 31739 sdud ydoruhv dflpd gh 315/

hod vhuld xpd hvfrokd pxlwr jurvvhlud sdud uhsuhvhqwdu qrvvr frqkhflphqwr gd

pruwdolgdgh lqidqwlo hp Plqdv Jhudlv1 Xp srxfr gh whqwdwlyd h huur/ dx{loldgr

sru glvfxvvøhv frp hslghlroöjrv/ ohyd d xpd glvwulexlêær pxlwr pdlv uhdolvwd/ d gh

xpd jdpd frp sduåphwurv � @ 4=5 h � @ 57 txh srvvxl ydoru hvshudgr 3138 h

Page 51: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

79 FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

teta

dens

idad

e G

ama(

2,10

)

0.0 0.2 0.4 0.6 0.8 1.00

12

3

Iljxud 617= Ghqvlgdgh gh suredelolgdgh xpd glvwulexlêær Jdpd+5/43,1

ghvylr sdguær 31379 frp ghqvlgdgh uhsuhvhqwdgd qr juä�fr gd Iljxud 618 dedl{r1

Qhvwd qryd glvwulexlêær/ d fkdqfh gh revhuyduprv xp ydoru wær h{wuhpr txdqwr

315 ì dshqdv 31346/ qær lpsrvvðyho pdv ud}rdyhophqwh lpsuryäyho1

Xpd gdv irqwhv gh judqgh glvfxvvær flhqwð�fd qr sdvvdgr hud txh/ frpr hv0

wd glvwulexlêær h{suhvvd d lqfhuwh}d gh xp revhuydgru vreuh r ihq÷phqr +d wd{d

vxemdfhqwh,/ d lqihuíqfld sdvvdyd d id}hu vhqwlgr dshqdv sdud hoh h sdud rxwurv

txh frpsduwlokdydp gd phvpd h{suhvvær gd lqfhuwh}d1 Sru rxwur odgr/ d ghwhu0

plqdêær gh irupd suìyld ã revhuydêær grv gdgrv grv sduåphwurv � h � +rx rxwurv

sduåphwurv ghwhuplqdqwhv gh dojxpd rxwud glvwulexlêær txh sxghvvh vhu hvfroklgd

dr lqyìv gd glvwulexlêær jdpd, ì ixqgdphqwdo sdud rv uhvxowdgrv �qdlv h/ gdgr vhx

fduäwhu vxemhwlyr/ h r pìwrgr ed|hvldqr �fdyd qhfhvvduldphqwh qxpd srvlêær gh0

ihqvlyd sdud frqyhqfhu revhuydgruhv fìwlfrv txh ì/ d�qdo/ xp grv judqgh remhwlyrv

flhqwð�frv1 Sru fdxvd glvwr/ r pìwrgr ed|hvldqr hpsðulfr yhlr frpr xpd vroxêær

txh hylwd d hvshfl�fdêær suìyld ghvwhv sduåphwurv gd glvwulexlêær gdv wd{dv �l*v1

Page 52: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6171 HVWLPDÊÆR ED\HVLDQD HPSÐULFD 7:

teta

dens

idad

e G

ama(

1.2,

24)

0.0 0.05 0.10 0.15 0.20

05

1015

Iljxud 618= Ghqvlgdgh gh xpd glvwulexlêær jdpd frp sduåphwurv � @ 4=5 h � @ 571

61716 Hvwlpdgru ed|hvldqr olqhdu öwlpr

Yrowdqgr dr fdvr hp txh �l> l @ 4> = = = > q vær lqghshqghqwhv h srvvxhp xpd glv0

wulexlêær gh suredelolgdgh frpxp frp ydoru hvshudgr �� h ydul�åqfld �5�/ r remhwlyr

uhvlgh hp hvwlpdu hvwdv wd{dv ghvfrqkhflgdv frp edvh qrv gdgrv revhuydgrv1 Fr0

pr h{lvwh lqwhuhvvh hp wrgdv dv wd{dv gh qrvvr pdsd vlpxowdqhdphqwh/ h qær

qxpd wd{d gh xpd äuhd sduwlfxodu/ dgrwd0vh frpr fulwìulr gh hvfrokd sdud xp hv0

wlpdgru dtxhoh txh plqlpl}h d vrpd grv huurv txdguäwlfrv gh hvwlpdêær gdv äuhdvSlH+�l � a�l,

51 Doìp glvwr/ frpr rv sduåphwurv �l vær yduläyhlv dohdwöuldv/ d hv0

shudqêd qhvwd vrpd ì wrpdgd frp uhvshlwr d dperv/ a�l h �l1 Ì ehp frqkhflgr txh

r hvwlpdgru gh Ed|hv öwlpr a�l sdud hvwh sureohpd ì d hvshudqêd d sruwhulrul gh

�l frqglflrqdophqwh hp wrgdv dv revhuydêøhv |4> ===> |q1 Hp prghorv vlpsohv/ srgh

vhu srvvðyho rewhu hvwh hvwlpdgru gh Ed|hv öwlpr pdv hp vlwxdêøhv pdlv frpsoh{dv

lvwr ì txdvh lpsrvvðyho1 Ydprv yhu xp h{hpsor hp txh hvwh fäofxor vlpsohv ì srv0

vðyho1 Doìp glvwr/ hvwh vhuä xp h{hpsor hp txh r hvwlpdgru hpsðulfr gh Ed|hv

wdpeìp srgh vhu rewlgr idflophqwh1

Page 53: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7; FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

61717 Xp h{hpsor vlpsohv

Frpr qr fdvr gd pruwdolgdgh lqidqwlo/ vxsrqkd txh/ gdgdv dv wd{dv vxemdfhqwhv

�l> l @ 4> = = = > q/ dv revhuydêøhv vær frqwdjhqv prghodgdv frpr |lm�l�Srlvvrq+ql�l,rqgh ql ì r qýphur gh fuldqêdv qdvflgdv ylydv qd äuhd l1 Vxsrqkd wdpeìp txh

dv wd{dv �l> l @ 4> = = = > q vær lqghshqghqwhv h vhjxhp xpd glvwulexlêær Jdpd

frp sduåphwur gh irupd � h gh hvfdod �1 Ì xp h{hufðflr frqkhflgr gh lqihu0

íqfld prvwudu txh d glvwulexlêær qær frqglflrqdo gh |l ì xpd elqrpldo qhjdwlyd

frp hvshudqêd ql�@� h ydulåqfld ql�@�. q5l�@�51 Doìp glvwr/ d glvwulexlêær

frqmxqwd d srvwhulrul grv �l*v ì dtxhod gh glvwulexlêøhv Jdpd lqghshqghqwhv h

�lm|4> ====> |q�Jdpd+|l . �> ql . �, frp hvshudqêd frqglflrqdo ljxdo d H+�lm|l, @+|l .�,@+ql . �,/ xp ydoru txh hvwä hqwuh d wd{d euxwd xvxdo |l@ql h d hvshudqêd

d sulrul �@�1

Hvwd hvshudqêd d srvwhulrul +|l . �,@+ql . �, ì r hvwlpdgru öwlpr gh Ed|hv

sdud d shugd txdguäwlfd1 Hvwlpdwlydv edvhdgdv hp xp judqgh qýphur gh pruwhv

revhuydgdv |l �fdp suö{lpdv gd wd{d euxwd hqtxdqwr txh dtxhodv edvhdgdv hp xp

shtxhqr qýphur gh pruwhv whqghp d �fdu pdlv suö{lpdv gd hvshudqêd d sulrul1

R hvwlpdgru gh Ed|hv e�l @ +|l . �,@+ql . �, ghshqgh gh � h �/ rv txdlv

ghyhp frqkhflgrv sdud txh hoh srvvd vhu fdofxodgr1 Frpr hvwhv grlv ydoruhv vær

hvwdehohflgrv d sulrul h pxlwdv yh}hv kä glyhujíqfld rx lqvhjxudqêd vreuh rv ydoruhv

d vhuhp hvwdehohflgrv/ r pìwrgr ed|hvldqr hpsðulfr surfxud hvwlpä0orv d sduwlu

grv suösulrv gdgrv1 Frpr d glvwulexlêær pdujlqdo grv gdgrv/ d elqrpldo qhjdwlyd

qhvwh h{hpsor/ wdpeìp ghshqgh gh � h � ì srvvðyho fdofxodu hvwlpdwlydv e� h e� sdud

hvwhv sduåphwurv edvhdgr qdv revhuydêøhv |4> ====> |q1 D vhjxlu/ r pìwrgr ed|hvldqr

hpsðulfr vxevwlwxl rv sduåphwurv � h � qd iöupxod gd hvshudqêd d srvwhulrul shodv

vxdv hvwlpdwlydv e� h e�1H{vlvwhp gxdv irupdv kdelwxdlv gh hvwlpdu � h � = srgh0vh xvdu r pìwrgr pdlv

vlpsohv gh prphqwrv rx r pìwrgr pdlv h�flhqwh gh pä{lpd yhurvvlplokdqêd1 Sdud

hvwh ýowlpr pìwrgr/ d ixqêær gh orj0yhurvvlplokdqêd ì gdgd sru

O+�> �, @[l

�orj

�+|l .�,

�+�,. � orj+�,� +|l . �, orj +ql . �,

�txh ghyh vhu pd{lpl}dgd qxphulfdphqwh1 Fod|wrq h Ndogru +4<;:, iruqhfhp wdp0

Page 54: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6171 HVWLPDÊÆR ED\HVLDQD HPSÐULFD 7<

eìp rxwudv dowhuqdwlydv pdlv vlpsohv sdud hvwlpdu e� h e� qhvwh fdvr hvshfð�fr1

61718 Hvwlpdgruhv gh Ed|hv olqhduhv öwlprv

Frpr ylprv dqwhulruphqwh/ r hvwlpdgru ul @ |l@ql qær ì xpd erd hvfrokd h rv

hvwlpdgruhv gh Ed|hv öwlprv frp rv sduåphwurv hvwlpdgrv hpslulfdphqwh d sduwlu

gd glvwulexlêær pdujlqdo grv gdgrv vær xpd erd vroxêær dowhuqdwlyd 1 Hqwuhwdq0

wr/ dshqdv hp vlwxdêøhv vlpsohv ì srvvðyho fdofxodu hvwhv hvwlpdgruhv ed|hvldqrv

hpsðulfrv1 Dvvlp/ hvwlpdgruhv olqhduhv gh Ed|hv sdvvdudp d vhu xwlol}dgrv srlv

r hvwlpdgru öwlpr qhvwd fodvvh ghshqgh dshqdv grv grlv sulphlurv prphqwrv gd

glvwulexlêær d sulrul1 Pxlwdv yh}hv hvwhv grlv prphqwrv d sulrul srghp vhu hvwl0

pdgrv d sduwlu grv gdgrv xvdqgr dojxpd uhodêær hqwuh rv prphqwrv d sulrul grv

sduåphwurv h d glvwulexlêær pdujlqdo grv gdgrv1

Frpr dqwhv qr fdvr gd pruwdolgdgh lqidqwlo/ vxsrqkd txh/ gdgdv dv wd{dv

vxemdfhqwhv �l> l @ 4> = = = > q/ dv frqwdjhqv vær |lm�l�Srlvvrq+ql�l, h txh dv wd{dv

�l> l @ 4> = = = > q vær lqghshqghqwhv pdv qær dvvxplprv qdgd dfhufd ghvwd glv0

wulexlêær d sulrul d qær vhu txh hod srvvxl pìgld h ydulåqfld gdgdv sru �� h �5�/

uhvshfwlydphqwh1

R hvwlpdgru olqhdu öwlpr gh Ed|hv ì gdgr sru

a�l @ zl ul . +4�zl,�� +614,

rqgh zl @ �5�@Ydu+ul, hvwä hqwuh 3 h 4 +Jul!q dqg Nuxwfknr�/ 4<:4,1 Lvwr ì/ r

hvwlpdgru 614 ì xpd pìgld srqghudgd hqwuh ul h ��1

Sdud hqwhqghu xp srxfr phokru hvvd pìgld/ revhuyh txh Ydu+ul, @ Ydu+H+ulm�l,,.H+Ydu+ulm�l,,1 Qr hqwdqwr/ ul ì qær0ylfldgr sdud hvwlpdu d wd{d ghvfrqkhflgd

�l fruuhvsrqghqwh1 Hqw�ær/ YduH+ul�l, @ Ydu+�l, @ �5� h/ ghvvh prgr/ zl @

�5�@+�5� .H+Ydu+ulm�l,,1

Ilfd fodur txh r hihlwr gr hvwlpdgru 614 gh Ed|hv ì frqwudlu r hvwlpdgru xvxdo ul

hp gluhêær dr ydoru hvshudgr �� grv �l gh dfrugr frp r ydoru gh H+Ydu+ulm�l,,1 Xpjudqgh ydoru lqglfd txh/ hp pìgld/ ul ì xp hvwlpdgru lqvwäyho h/ frpr frqvhtxíq0

fld/ r hvwlpdgru whuä zl suö{lpr gh }hur surgx}lqgr xpd judqgh frqwudêær1 Vh

Page 55: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

83 FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

H+Ydu+ulm�l,, ì shtxhqr hqwær/ hp pìgld/ ul whp shtxhqd ydulåqfld/ zl ì suö{lpr

gh 4 h d frqwudêær ì wdpeìp shtxhqd1

Hp uhvxpr/ d hvwlpdwlyd a�l hp 614 ì xp ydoru lqwhuphglä ulr hqwuh d wd{d

ul gd äuhd h r ydoru hvshudgr �� gdv wd{dv ghvfrqkhflgdv1 R shvr gh fdgd xpd

qd hvwlpdwlyd ghshqgh gd lqfhuwh}d gd hvwlpdwlyd ul= vh hvvd iru xpd wd{d frp

shtxhqd yduldelolgdgh/ ul sudwlfdphqwh qær ì dowhudgd1 Vh/ sru rxwur odgr/ ul wlyhu

judqgh ydulåqfld hp pìgld/ hqwær srxfr shvr ì dwulexðgr dr lqvwäyho ul wrpdqgr

a�l pdlv su�ö{lpr gr ydoru hvshudgr �� gh xpd äuhd hvfroklgd dr dfdvr1

61719 Hvwlpdgru öwlpr olqhdu ed|hvldqr hpsðulfr

Pduvkdoo +4<<4, surs÷v xp pìwrgr ed|hvldqr hpsðulfr h{wuhpdphqwh vlpsohv gh

vhu lpsohphqwdgr h txh qær vxsøh qhqkxpd glvwulexlêær hvshfð�fd sdud rv �l1 Hoh ì

edvhdgr qr pìwrgr grv prphqwrv dsolfdgr d glvwulexlêær pdujlqdo gdv frqwdjhqv1

Dv i�öupxodv eävlfdv vær=

a�l @ Fl ul . +4� Fl, ap

rqgh ap @S

l|l@S

lql/ d wd{d joredo/ h

Fl @v5 � ap@�q

v5 � ap@�q. ap@ql

frp �q @S

l @Q / r q�xphur pìglr gh shvvrdv hp ulvfr/ h v5 @S

l ql +ul � ap,5@q/

rqgh q @S

l ql1 Srgh dfrqwhfhu gh v5 ? ap@�q1 Qhvvh fdvr/ a�l @ ap1

Qr fdvr gd pruwdolgdgh lqidqwlo hp Vær Sdxor/ dsolfdqgr hvwh pìwrgr sursrvwr

sru Pduvdkoo surgx} r pdsd gd Iljxud 619 qd phvpd hvfdod hp txh irl ihlwr r pdsd

gdv wd{dv euxwdv qd Iljxud 6141 Revhuyh d hqruph frqwudêær gdv wd{dv hvwlpdgdv

shor pìwrgr ed|hvldqr prvwudqgr txh erd sduwh gd yduldelolgdgh suhvhqwh qdv

wd{dv euxwdv srgh vhu fuhglwdgd d idwruhv dohdwöulrv qær dvvrfldgrv frp rv ulvfrv

vxemdfhqwhv1

D Iljxud 61: prvwud r phvpr pdsd pdv xwlol}dqgr xpd hvfdod glihuhqwh gd wd{d

euxwd/ pdlv dsursuldgd sdud d shtxhqd yduldêær gdv wd{dv ed|hvldqdv hpsðulfdv1

Page 56: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

6171 HVWLPDÊÆR ED\HVLDQD HPSÐULFD 84

Iljxud 619= Pdsd gdv wd{dv ed|hvldqdv hpsðulfdv gh pruwdolgdgh lqidqwlo hp Vær

Sdxor hp 4<<;1 Hvfdod ì d phvpd gr pdsd gh wd{dv euxwdv1

Revhuyh txh dlqgd kä h{lvwh xp erd grvh gh yduldêær hvsdfldo qr pdsd h txh hod

pxlwr pdlv fodud djrud1

6171: Hvwlpdgru lqwhludphqwh ed|hvldqr

R hvwlpdgru ed|hvldqr hpsðulfr gh Pduvkdoo +4<<4, ì pxlwr iäflo gh vhu xwlol}dgr

h surgx} erdv hvwlpdwlydv srqwxdlv/ frpsduäyhlv äv grv pìwrgrv lxqwhludphqwh

ed|hvldqrv1 Hqwuhwdqwr/ hoh srvvxl gxdv ghvydqwdjhqv qær frpsduwlokdgdv sru xp

pìwrgr sxudphqwh ed|hvldqr= hoh qær ljqrud d yduldelolgdgh lqwurgx}lgd qd hvwl0

pdêær grv sduåphwurv gd sulrul h qær olgd ehp frp d yduldelolgdgh grv hvwlpdgruhv

surgx}lgrv> doìp glvwr/ hoh qær srgh vhu jhqhudol}dgr sdud dv vlwxdêøhv ehp pdlv

frpsoh{dv/ frpr gh lqwhudêær hqwuh hvsdfr h whpsr/ txh frphfdp d jdqkdu d

dwhqêær grv shvtxlvdgruhv1 R dvvxqwr gr suö{lpr fdsðwxor ì xpd lqwurgxêær drv

pìwrgrv lqwhludphqwh ed|hvldqrv sdud d surgxêær gh pdsdv gh grhqêdv1

Page 57: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

85 FDSÐWXOR 61 PDSHDPHQWR GH GRHQÊDV

Iljxud 61:= Pdsd gdv wd{dv ed|hvldqdv hpsðulfdv gh pruwdolgdgh lqidqwlo hp Vær

Sdxor hp 4<<;1

Page 58: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

Fdsðwxor 7

����� ���������� ��

�������

714 R uhyhuhqgr Ed|hv qr �p gr vìfxor

Rv qryrv pìwrgrv sdud uhvroyhu sureohpdv hvwdwðvwlfrv wíp vlgr edvwdqwh lq x0

hqfldgrv shorv surfhglphqwrv frpsxwdflrqdlv prghuqrv1 Hvwhv qryrv pìwrgrv h

derugdjhqv h{ljhp srxfdv klsöwhvhv dfhufd gh glvwulexlêøhv h srghp vhu dsolfd0

grv d hvwlpdgruhv frpsolfdgrv1 Lvwr dxphqwd frqvlghudyhophqwh d srvvlelolgdgh

gh h{sorudu rv gdgrv h rewhu lqihuíqfldv yäolgdv vhp d suhrfxsdêær kdelwxdo hp

wudedokdu frp prghorv wudwäyhlv pdwhpdwlfdphqwh1 Hp dojxqv dvshfwrv/ pìwrgrv

frpsxwdflrqdlv vxevwlwxðudp pìwrgrv gh dqäolvh gh gdgrv wudglflrqdlv1 Hqwuh0

wdqwr/ d pdwhpäwlfd dlqgd ì h{wuhpdphqwh uhohydqwh sdud dqäolvh gd h�flíqfld h

frqyhujíqfld grv dojrulwprv1 Pìwrgrv gh Prqwh Fduor/ dojrulwpr HP/ errwvwuds/

uhjuhvvær qær0sdudpìwulfd h äuyruhv gh fodvvl�fdêær vær dojxqv grv h{hpsorv pdlv

surplvvruhv h srsxoduhv gh ghvhqyroylphqwrv gd phwrgrorjld hvwdwðvwlfd lqwhqvlyrv

frpsxwdflrqdophqwh1

Xpd fodvvh gh pìwrgrv frpsxwdflrqdlv/ fkdpdgd dojrulwprv gh Prqwh Fduor

yld Fdghldv gh Pdunry/ lqlfldophqwh ghvhqyroylgd hp iðvlfd hvwdwðvwlfd qd gìfdgd

gh 83 +Phwursrolv hw do1/ 4<86,/ jdqkrx hqruph srsxodulgdgh d sduwlu gr duwljr gh

86

Page 59: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

87 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

Jhpdq h Jhpdq +4<;7,1 R sulqflsdo remhwlyr ghvwhv pìwrgrv ì jhudu xpd dprvwud

gh revhuydêøhv ghshqghqwhv gh xpd glvwulexlêær pxowlyduldgd frp ghqvlgdgh fs+{,/

srvvlyhophqwh edvwdqwh frpsoh{d h frqkhflgd d phqrv gd frqvwdqwh gh lqwhjudêær

f1 Dv revhuydêøhv vær ghshqghqwhv srlv hodv vær jhudgdv frpr hvwdgrv vxfhvvlyrv

gh xpd uhdol}dêær gh fhuwd fdghld gh Pdunry1

D lqihuíqfld ed|hvldqd dwì uhfhqwhphqwh hud gh dsolfdêær gliðflo hp vlwxdêøhv

uhodwlydphqwh frpsoh{dv sru fdxvd gdv hqruphv gl�fxogdghv qd rewhqêær gh ghqvl0

gdghv d srvwhulrul1 Frp r dgyhqwr ghvwhv dojrulwprv gh Prqwh Fduor yld Fdghldv gh

Pdunry/ d rewhqêær gd srvwhulrul irl vlpsol�fdgd wær gudpdwlfdphqwh txh wruqrx0

vh xp h{hufðflr vlpsohv sdud txdotxhu hvwxgdqwh prghodu gh irupd uhodwlydphqwh

frpsoh{d xp frqmxqwr gh gdgrv h id}hu lqihuíqfldv xwlol}dqgr hvwh pìwrgr1 Sdud

wruqdu hvwd derugdjhp pdlv srsxodu dlqgd/ h{lvwh xp vriwzduh judwxlwr fkdpdgr

EXJV 0 Ed|hvldq dqdo|vlv Xvlqj Jleev Vdpsohu/ wruqdqgr h{wuhpdphqwh iäflo d

rewhqêær ghvwd srvwhulrul1

Wxgr lvwr wruqrx d derugdjhp ed|hvldqd wær srsxodu txh d gìfdgd gh <3/

ihfkdqgr r vìfxor +h r ploíqlr, irl fkdpdgd gh gìfdgd ed|hvldqd1 Duwljrv ed|hvldqrv

frqwhqgr dqäolvh gh gdgrv frp prghorv edvwdqwh frpsoh{rv lqxqgdudp rv sulq0

flsdlv shulöglfrv gh hvwdwðvwlfd1 D Hvwdwðvwlfd Hvsdfldo qær �frx lpxqh d hvwd

rqgd gh lqrydêøhv1 Hp sduwlfxodu/ d derugdjhp Ed|hvldqd sdud r pdshdphqwr gh

grhqêdv ì dwxdophqwh d phwrgrorjld suhihulgd h pdlv xvdgd1 Dv gxdv sulqflsdlv

ud}øhv vær dv vhjxlqwhv= hod srgh prghodu vlwxdêøhv h{wuhpdphqwh frpsoh{dv lq0

frusrudqgr uhvwulêøhv rx ghshgíqfldv hvwrfävwlfdv gh irupd vlpsohv h hod srvvxl xp

pìwrgr frpsxwdflrqdo gh hvwlpdêær/ rv dojrulwprv gh Prqwh Fduor yld Fdghldv gh

Pdunry/ txh srgh vhu dsolfdgr gh irupd pdlv rx phqrv dxwrpäwlfd sdud rewhqêær

gd lqihuíqfld vreuh rv sduåphwurv grv prghorv1 Qhvwh fdsðwxor ydprv h{sru hvwh

pìwrgr ed|hvldqr gh pdshdphqwr gh grhqêdv dvvxplqgr txh r ohlwru srvvxl xp

frqkhflphqwr gh lqihuíqfld ed|hvldqd h qrêøhv eävlfdv gh dojxqv dojrulwprv gh

Prqwh Fduor yld Fdghldv gh Pdunry1

Page 60: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7151 PRGHOR KLHUÄUTXLFR ED\HVLDQR SDUDPDSDV GH GRHQÊDV88

715 Prghor klhuäutxlfr ed|hvldqr sdud pdsdv gh

grhqêdv

Ydprv vxsru txh h{lvwhp q äuhdv jhrjuä�fdv vre frqvlghudêær h fdgd xpd ghodv

srvvxl xpd phglgd gh ulvfr #l> l @ 4> = = = >Q / txh ghyh vhu hvwlpdgd1 Hvwhv ulvfrv

srghp vhu devroxwrv/ qr vhqwlgr gh wd{dv shu fdslwd rx sru 433 plo rx/ dowhu0

qdwlydphqwh/ hohv srghp vhu uhodwlyrv d dojxp qðyho/ jhudophqwh dtxhoh gr ydoru

hvshudgr Hl frqvlghudqgr r ulvfr gh xpd uhjlær pdlru hqjoredqgr d uhjlær hp hv0

wxgr1 Rv gdgrv gd uhjlær l fruuhvsrqghp drv qýphurv gh fdvrv |l qxpd srsxodêær

gh wdpdqkr ql1 D lqihuíqfld ed|hvldqd ì edvhdgd qd glvwulexlêær d srvwhulrul gh

#=

i+#m|, 2 o+|4> ===> |qm#, i+#,

rqgh o+|4> ===> |qm#, ì d ixqêær gh yhurvvplokdqêd h i+#, ì d glvwulexlêær d sulrul

gr yhwru gh sduåphwurv #@ +#4> = = = > #q,1 Frqglflrqdophqwh hp #4> = = = > #q/ rv

ydoruhv |4> = = = > |Q vær vxsrvwrv lqghshqghqwhv frp glvwulexlêær gh Srlvvrq frp

pìgld ql #l/ qr fdvr gh wd{dv/ rx pìgld Hl #l/ qr fdvr gh ulvfrv uhodwlyrv/ rqgh

Hl ì r ydoru hvshudgr vre d klsöwhvh gh ulvfr frqvwdqwh qr hvsdêr qdv glyhuvdv

fodvvhv gh lgdgh h vh{r1 D prghodjhp gd glvwulexlêær d sulrul i+#, shuplwh lqwur0

gx}lu ghshqgíqfld hvsdfldo hqwuh rv ulvfrv gh prgr txh uhjløhv suö{lpdv whqghp

d whu ulvfrv vhphokdqwhv1 Hvwd ghshqgíqfld dsduhfh vre d irupd gh xpd hvwux0

wxud Pdunryldqd +Fod|wrq ) Ndogru/ 4<;:, h r pìwrgr gh hvwlpdêær ì lqwhqvlyr

frpsxwdflrqdophqwh xwlol}dqgr0vh rv dojrulwprv gh Prqwh Fduor yld Fdghldv gh

Pdunry +Ehvdj hw do1/ 4<<4,1

Frp d glvwulexlêær gh Srlvvrq sdud dv revhuydêøhv h frp rv sduåphwurv uhsuh0

vhqwdqgr ulvfrv uhodwlyrv/ d yhurvvlplokdqfd gh #4> = = = > #q ì gdgd sru

o+|4> ===> |qm#, @q\l@4

+#lHl,|l

|l$h{s +�#lHl, +714,

Qr fdvr gh grv sduåphwurv uhsuhvhqwduhp wd{dv shu fdslwd/ edvwd vxevwlwxlu

Hl sru ql1 Gr srqwr gh ylvwd gd dqäolvh hvwdwðvwlfd/ hvwd glihuhqfd ì lpdwhuldo/

Page 61: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

89 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

dihwdqgr dshqdv d lqwhusuhwdêær gdgd drv sduåphwurv1 Dvvlp/ qr uhvwdqwh ghvwh

fdsðwxor/ ydprv dvvxplu txh rv sduåphwurv uhsuhvhqwdp ulvfrv uhodwlyrv h txh d

yhurvvlplokdqfd ì gdgd shod h{suhvvær 7141 R fdvr gh wd{dv srgh vhu ghulydgr

idflophqwh shor ohlwru1

Dvvlp/ sduwh gd yduldêær qrv gdgrv revhuydgrv h hp hvwlpdwlydv vlpsohv gh #l/

wdlv frpr d VPU @ |l@Hl/ ì ghylgr ã yduldêær qrv ulvfrv uhodwlyrv #l1 Hqwuhwdq0

wr/ r prghor suredeloðvwlfr 714 prvwud txh xpd sduwh dglflrqdo gd yduldêær gdv

revhuydêøhv ì ghylgr d xpd xwxdêær dohdwöuld +vre d irupd gh xpd glvwulexlêær

Srlvvrq, vreuhsrvwd dv glihuhqfdv qær revhuydgdv grv ulvfrv vxemdfhqwhv #4> = = = > #q1

Dr lqyìv grv ulvfr uhodwlyr #l/ qöv wudedokdprv frp r vhx orjdulwpr/ �l @

orj +#l,/ xpd wudqvirupdêær edvwdqwh frpxp hp hvwxgrv hvwdwðvwlfrv srlv hoh ì r

sduåphwur qdwxudo gd glvwulexlêær gh Srlvvrq/ ylvwd frpr xp phpeur gd idpðold

h{srqhqfldo gh glvwulexlêøhv1 Lvwr wud} dojxpdv ydqwdjhqv whöulfdv srlv whuplqdprv

frp xp frqmxqwr gh hvwdwðvwlfdv vx�flhqwhv vlpsohv txh qær ghshqghp gr wdpdqkr

gd dprvwud/ doìp gh wud}hu qxpìulfdv vlpsol�fdêøhv sdud rv dojrulwprv1

71514 Ghfrpsrvlêær gr ulvfr uhodwlyr

R duwljr Ehvdj hw do1 +4<<4, lqwurgx}lx r srsxodu prghor hp txh r orjdulwpr gr

ulvfr uhodwlyr �l ì d vrpd gh grlv frpsrqhqwhv lqghshqghqwhv= r sulphlur uhjlvwud

r hihlwr dohdwöulr qær hvsdfldo/ uhsuhvhqwdgr sru !l/ hqtxdqwr txh r vhjxqgr ì r

hihlwr dohdwöulr hvsdfldo gd äuhd l/ uhsuhvhqwdgr sru �l1 Lvwr ì/ orj#l @ �l @ !l.�l1

D lqwhqêær ghvwhv dxwruhv irl ghfrpsru d yduldêær gr ulvfr uhodwlyr hp gxdv

sduwhv1 D sulphlud sduwh/ uhsuhvhqwdgd shor frpsrqhqwh ! @ +!4> ===> !q, > qær

srvvxl xpd hvwuxwxud hvsdfldo h uhsuhvhqwd hihlwrv gh shtxhqd hvfdod/ glihuhqfdv

gh äuhd sdud äuhd txh qær xowudsdvvdp vxdv iurqwhludv jhrjuä�fdv1 Hvwhv hihlwrv

srghuldp vhu dêøhv gh vdýgh sýeolfd rx fdudfwhuðvwlfdv hfrq÷plfdv rx vrfldlv orfdlv

qær frpsduwlokdgdv shodv äuhdv yl}lqkdv1 Dvvlp/ hohv vær hihlwrv hvshfð�frv gh fdgd

äuhd frqvlghudgd lqglylgxdophqwh h srghp vhu prghodgrv frpr hihlwrv dohdwöulrv

lqghshqghqwhv1

D vhjxqgd sduwh/ uhsuhvhqwdgd shor frpsrqhqwh � @ +�4> ===> �q,/ srvvxl xpd

hvwuxwxud hvsdfldo h ì gh�qlgd gh prgr d hvwlpxodu äuhdv yl}lqkdv d vhuhp pdlv

Page 62: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7151 PRGHOR KLHUÄUTXLFR ED\HVLDQR SDUDPDSDV GH GRHQÊDV8:

vhphokdqwhv/ hp whuprv gr vhx ulvfr uhodwlyr/ gr txh gxdv äuhdv hvfroklgdv dr dfdvr

qr pdsd1 Hvwh frpsrqhqwh uhsuhvhqwd hqwær hihlwrv gh odujd hvfdod/ gh hvfrsr

jhrjuä�fr pdlru txh dv iurqwhludv gdv äuhdv txh hvwær vhqgr frqvlghudgdv1 Pxlwrv

yduläyhlv revhuydgdv rx qær revhuydgdv txh dihwdp rv ulvfrv ã vdýgh srvvxhp hvwd

fdudfwhuðvwlfd1 Sru h{hpsor/ fdudfwhuðvwlfdv dpelhqwdlv h d hvwuxwxud surgxwlyd/ hp

jhudo/ pxgdp vxdyhphqwh qr hvsdêr h dvvlp äuhdv suö{lpdv whqghp d vhu vlploduhv

qhvwh wlsr gh yduläyhlv1

Hp whuprv gh prghodjhp/ rv hohphqwrv gr sulphlur frpsrqhqwh srvvxhp glv0

wulexlêøhv qrupdlv lqghshqghqwhv frppìgld 3 h ydulåqfld 4@�!1 Dvvlp/ +!4> ===> !q,

ì xpd qrupdo pxowlyduldgd frpsrvwd gh whuprv lqghshqghqwhv1 Hvwd glvwulexlêær

ghshqgh gh xp sduåphwur ixqgdphqwdo/ �!/ txh hp jhudo ì ghvfrqkhflgr1 Hvwh

sduåphwur frqwurod r judx gh glvshuvær grv hihlwrv dohdwöulrv qær hvwuxwxudgrv

hvsdfldophqwh1 Vh �! ì uhodwlydphqwh shtxhqr/ hqwær kdyhuä xpd judqgh yduldelol0

gdgh grv hihlwrv dohdwöulrv +!4> ===> !q, hp wruqr gh vxd pìgld frpxp ljxdo d }hur/

vljql�fdqgr xpd judqgh yduldelolgdgh grv ulvfrv uhodwlyrv1 Dowhuqdwlydphqwh/ vh

�! ì uhodwlydphqwh judqgh/ lvwr lpsolfd qxpd shtxhqd yduldêær ghvwh frpsrqhqwh

gr ulvfr uhodwlyr hp wruqr gh }hur sdud wrgdv dv äuhdv 1 Qrwh txh hvwd yduldelo0

lgdgh qær whp qhqkxpd hvwuxwxud hvsdfldo/ rx vhmd/ ì xp prghor gh sxur hihlwr

dohdwöulr1 Ghvwd irupd/ r pdlv fruuhwr ì lqglfdu txh d glvwulexlêær ghvwh frpsr0

qhqwh hvwä gh�qlgd frqglflrqdophqwh qr ydoru gh �!1 Lvwr ì/ gdgr r ydoru gh �!/

i +!4> ===> !qm�!, ì frpsrvwd gh qrupdlv l1l1g1 frp pìgld 3 h ydulåqfld �!1

D glvwulexlêær frqmxqwd gr vhjxqgr frpsrqhqwh � @ +�4> ===> �q, whp xpd hv0

wuxwxud hvsdfldo h ì gh�qlgd gh prgr d hvwlpxodu äuhdv yl}lqkdv d vhuhp pdlv

vhphokdqwhv/ hp whuprv gr vhx ulvfr uhodwlyr/ gr txh gxdv äuhdv hvfroklgdv dr dfd0

vr qr pdsd1 D glvwulexlêær hvfroklgd ì wlslfdphqwh xp fdpsr dohdwöulr gh Pdunry

qrupdo h vhuä ghvfulwr hp ghwdokhv qd suö{lpd vhêær1 Sru krud/ ydprv dshqdv gl}hu

txh/ doìp gd gh�qlêær gh xpd hvwuxwxud gh yl}lqkdqfd hvsdfldo/ hod srgh ghshq0

ghu gh xp sduåphwur ghvfrqkhflgr dglflrqdo ��/ lqyhuvdphqwh uhodflrqdgr frp

d yduldelolgdgh gh �4> ===> �q1 Hvwh sduåphwur ì ixqgdphqwdo srlv hoh phgh r judx

gh vlplodulgdgh hvsdfldo hqwuh hvwhv frpsrqhqwhv grv ulvfr uhodwlyr1 Qd suö{lpd

vhêær/ sdud hylwdu vreuhfduuhjdu d qrwdêær/ ydprv rplwlu hvwh frqglflrqdphqwr

Page 63: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8; FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

hvfuhyhqgr dshqdv i +�4> ===> �q, dr lqyìv gh i +�4> ===> �qm� �,

71515 Glvwulexlêær grv Klshusduåphwurv

Fdgd xpd gdv sulrulv grv frpsrqhqwhv � @ +�4> ===> �q, h ! @ +!4> ===> !q, ghshqgh

gh sduåphwurv/ �! h ��/ doìp gh rxwurv dglflrqdlv txh srghp vhu lqwurgx}lgrv

hp prghorv pdlv frpsolfdgrv1 Hvwhv sduåphwurv/ fkdpdgrv gh klshusduåphwurv/

vær prghodgrv sru rxwud glvwulexlêær/ fkdpdgd gh klshusulrul/ mä txh hod vh uhihuh

drv sduåphwurv gd glvwulexlêær gd sulrul grv sduåphwurv gd yhurvvlplokdqêd1 Rv

sduåphwurv gd sulrul vær fkdpdgrv gh sduåphwurv gh sulphlur qðyho hqtxdqwr txh

rv klshusduåphwurv vær rv gh vhjxqgr qðyho1

Wlslfdphqwh/ hvfrokh0vh xpd glvwulexlêær jdpd �+�> �, frp � vhqgr hvfroklgr

ehp shtxhqr wdo frpr � @ 43�6 sdud dperv rv klshusduåphwurv/ doìp gh vxsru

txh hodv vær lqghshqghqwhv1 Proolì +4<<8, h Ehuqdglqhool ) Prqwrprool +4<<5,

h Ehuqdglqhool hw do +4<<8e, vxjhuhp hvwudwìjldv glihuhqwhv sdud hvfrokhu hvwdv

klshusulrulv1

71516 Glvwulexlêær d Srvwhulrul

Whqgr rv hohphqwrv dflpd/ ì srvvðyho hvfuhyhu d glvwulexlêær d srvwhulrul grv

sduåphwurv h grv klshusduåphwurv d phqrv gh xpd frqvwdqwh gh lqwhjudêær1 Hvwd

glvwulexlêær ì sursruflrqdo dr surgxwr gdv glvwulexlêøhv grv wuív qðyhlv klhuäutxlfrv

glvfxwlgrv dqwhulruphqwh=

#q\l@4

+#lHl,|l

|l$h{s +�#lHl,

$i +!4> ===> !qm�!, i +�4> ===> �qm� �, i+�!,i+� �, +715,

Revhuyh txh dv glvwulexlêøhv sdud rv klshusduåphwurv/ i+�!, h i+� �,/ vær wrwdo0

phqwh hvshfl�fdgdv/ qær ghshqghqgr gh pdlv qhqkxpd txdqwlgdgh ghvfrqkhflgd1

Doìp glvwr/ #l @ h{s +�l, h{s +!l,1 Lqihol}phqwh/ d frqvwdqwh gh lqwhjudêær qær

srgh vhu rewlgd dqdolwlfdpdqwh1 Xwlol}d0vh hqwær pìwrgrv edvhdgrv hp Prqwh Fdu0

or yld Fdghldv gh Pdunry1 Ydprv wudwdu glvwr dsöv d suö{lpd vhêær rqgh ydprv gh0

wdokdu frpr srgh vhu hvshfl�fdgr r frpsrqhqwh hvsdfldo gd sulrul/ i +�4> ===> �qm��,/ghqrwdgr vlpsohvphqwh frpr i +�4> ===> �q, sdud idflolwdu d qrwdêær1

Page 64: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7161 SULRULV HVSDFLDOPHQWH HVWUXWXUDGDV 8<

716 Sulrulv Hvsdfldophqwh Hvwuxwxudgdv

71614 Fdpsrv dohdwöulrv gh Pdunry frpr glvwulexlêøhv d

sulrul

R frpsrqhqwh gr ulvfr txh srvvxl xpd hvwuxwxud hvsdfldo uhfheh xpd glvwulexlêær

gh suredelolgdgh fkdpdgd gh fdpsr dohdwöulr gh Pdunry1 Hod ì r htxlydohqwh

hvsdfldo gh xpd fdghld gh Pdunry qr whpsr h srvvxl d phvpd sursulhgdgh glvwlq0

wlyd gh wdlv fdghldv= d glvwulexlêær gr hvwdgr qxp gdgr orfdo l gdgr wrgr r uhvwr

gr pdsd ghshqgh dshqdv grv ydoruhv grv yl}lqkrv gh l1 Dvvlp/ qhvwd hvwuxwxud

gh suredelolgdgh ì qhfhvväulr hvwdehohfhu d hvwxwxud gh yl}lqkdqfd gr pdsd1 Qx0

pd fdghld gh Pdunry gh sulphlud rughp ghvhqyroyhqgr0vh qr whpsr/ rv yl}lqkrv

gd srvlêær whpsrudo l vær rv grlv prphqwrv lphgldwdphqwh dqwhfhghqwh h vxevh0

txhqwh/ l� 4 h l.4/ uhvshfwlydphqwh1 Hvwd hvwuxwxud gh yl}lqkdqêd ì vlpsohv sru

fdxvd gd xqlgluhflrqdolgdgh gr whpsr1 r txh qær ì r fdvr gr hvsdêr1

Frpr h{solfdprv qr Fdsðwxor BB/ ydprv uhsuhvhqwdu r pdsd h vxd d hvwuxwxud

gh yl}lqkdqfd dwudyìv gh xp judir rqgh dv duhvwdv srghp uhfhehu xp shvr dvvrfld0

gr frp r judx gh yl}lqkdqêd hqwuh dv äuhdv l h m1 Sru hqtxdqwr/ ydprv ghl{du hvwh

judir vhu wrwdophqwh duelwuäulr1 Pdlv dedl{r/ ydprv hvshfl�fdu xp srxfr phokru

dv uhvwulêøhv txh/ hp dojxqv fdvrv/ suhflvdp vhu lpsrvwdv1

Vhmd +�4> = = = > �q, @ � r yhwru gh sduåphwurv sdud r txdo txhuhprv gh�qlu

xpd glvwulexlêær gh suredelolgdgh frp xp fduäwhu hvsdfldo1 Frp xpd yl}lqkdqêd

lqgx}lgd shor judir/ ghqrwh sru Cl r frqmxqwr gh yl}lqkrv gd äuhd l1 Ghqrwh r

yhwru +�4> = = = > �l�4> �l.4> = = = > �n, sru ��l 1 D glvwulexlêær gh � srvvxl d sursulhgdgh

pdunryldqd/ h ì fkdpdgd gh fdpsr dohdwöulr gh Pdunry/ vh/ sdud wrgr l> l @

4> ===> q/ vxd glvwulexlêær frqmxqwd vdwlvid} d vhjxlqwh sursulhgdgh

i+�lm��l, @ i +�lm i�m wdlv txh m 5 Clj, +716,

Lvwr ì/ � srvvxl xpd glvwulexlêær gh Pdunry vh d glvwulexlêær gh �l frqglflrqd0

gd hp wrgr r uhvwdqwh gr pdsd iru d phvpd txh d glvwulexlêær gh �l frqglflrqdgd

dshqdv qrv ydoruhv gh äuhdv yl}lqkdv gh l1 Txhp ì gh�qlgr frpr yl}lqkr gh l ì/

hp sulqfðslr/ ghl{dgr d fulwìulr gr xvxäulr ghvwhv prghorv1 Qrwh txh gxdv äuhdv

Page 65: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

93 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

m h n/ dpedv shuwhqfhqwhv d Cl/ srghuær whu frqwulexlêøhv rx shvrv glihuhqwhv qd

ghwhuplqdêær gr ydoru gh �l1

Hvwdehohflgr xp vlvwhpd gh yl}lqkdqfd/ rewhu xpd glvwulexlêær frqmxqwd txh

vdwlvidêd d sursulhgdgh +716, qær sduhfh vhu xpd wduhid wulyldo1 D�qdo gh frqwdv/

d sursulhgdgh +716, uhihuh0vh d fdgd xpd gdv äuhdv l gr pdsd h sruwdqwr xpd

glvwulexlêær frqmxqwd pdunryldqd i+�, whuä txh vdwlvid}hu d xpd vlvwhpd gh q

htxdêøhv gd irupd +716,1 Gxudqwh d gìfdgd gh 83 h 93 vxujlx hqwær xp lpsruwdqwh

sureohpd whöulfr txh irl uhvsrqglgr shor Whruhpd gh Kdpphuvoh| h Fol�rug1 R

sureohpd srgh vhu frorfdgr qrv vhjxlqwhv whuprv= txdlv dv frqglêøhv qhfhvväuldv

h vx�flhqwhv sdud txh xpd glvwulexlêær frqmxqwd i+�, whqkd d sursulhgdgh pdunr0

yldqd +716, B Sdud uhvsrqghu d hvwd txhvwær suhflvdprv lqwurgx}lu dojxqv frqfhlwrv

dglflrqdlv1

71615 Whruhpd gh Kdpphuvoh| h Fol�rug

R pdsd vhuä lghqwl�fdgr frp xp judir h dv äuhdv frpsrqhqwhv gr judir vhuær

lghqwl�fdgdv frp r frqmxqwr gh qöv V gr judir1 Vhmd iCl> l @ 4> ===> qj xp vlvwhpd

gh yl}lqkdqêd qr frqmxqwr gh qöv V gr judir1 Xpd foltxh F ì xp vxefrqmxqwr gh

qöv wdlv txh txdlvtxhu grlv hohphqwrv vær yl}lqkrv1 Sru gh�qlêær/ r vxefrqmxqwr

qxor ! h rv vxefrqmxqwrv ilj irupdgrv sru xpd ýqlfd äuhd vær vhpsuh foltxhv1

Sru h{hpsor/ lpdjlqh xp pdsd irupdgr sru xp wdexohlur gh {dguh} frp dv

äuhdv vhqgr rv txdgudgrv sru rqgh dv shêdv flufxodp +yhu Iljxud BB,1 Hvwh ì xp

judir uhjxoduphqwh hvsdêdgr1 Frqvlghuh d yl}lqkdqêd gdgd shor prylphqwr gr

shær1 Lvwr ì/ rv yl}lqkrv gd äuhd2fdvd +{> |, vær dv äuhdv2fdvdv +{ � 4> |,> +{ .

4> |,> +{> | � 4,> +{> | . 4, lphgldwdphqwh dr qruwh/ vxo/ ohvwh h rhvwh gd äuhd hp

txhvwær1 Txdlv vær dv foltxhv gh�qlgdv qxp vlvwhpd gh yl}lqkdqêd gh�qlgr ghvwd

irupdB Ljqrudqgr rv dmxvwhv qhfhvväulrv sdud dv fdvdv qdv erugdv gr wdexohlur/

dv foltxhv sdud xpd äuhd2fdvd gr phlr gr wdexohlur/ vær r vxefrqmxqwr qxor !/ rv

vxefrqmxqwrv ilj/ l @ 4> ===> q/ h rv vxefrqmxqwrv gh sduhv gh äuhdv il> mj wdlv txh lh m vhmdp yl}lqkrv qr prylphqwr gr shær1 Vh d hvwuxwxud gh yl}lqkdqêd ì gh�qlgd

d sduwlu gr prylphqwr gr uhl +fdvd E qd Iljxud BB,/ hqwær grv vxefrqmxqwrv

Page 66: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7161 SULRULV HVSDFLDOPHQWH HVWUXWXUDGDV 94

BA

A= movimento do peao, B = movimento do rei

Iljxud 714= Pdsd uhjxodu dsuhvhqwdqgr gxdv srvvðyhlv irupdv gh gh�qlu yl}lqkdqfd/

CD h CE/ sdud dv äuhdv D h E1 D äuhd D srvvxl d yl}lqkdqfd gdgd shor prylphqwr

gr shær qr mrjr gh {dguh} h d äuhd E srvvxl d yl}lqkdqfd gdgd shor prylphqwr

gr uhl1

dqwhulruhv/ r frqmxqwr gdv foltxhv srvvxl wdpeìp rv sduhv gh äuhdv orfdol}dgrv hp

gldjrqdlv h dv wulsodv gh äuhdv gd irupd i+{> |,> +{> | . 4,> +{. 4> | . 4,j h vxdv

urwdêøhv gh <3r> 4;3r>5:3r h 693r1

Xp srwhqfldo ì xpd idpðold iXD = D � Vj gh ixqêøhv wdlv txh d ixqêær X! ì

lghqwlfdphqwh qxod h XD +�, ghshqgh dshqdv gd frq�jxudêær grv hohphqwrv gh �

hp D1 Lvwr ì/ XD srgh vhu hvfulwd frpr XD+�D, rqgh �D ì r yhwru frpsrvwr

dshqdv gdv frrughqdgdv gh � fruuhvsrqghqwhv drv qöv hp D1

Vhmd Y @ iCl> l @ 4> ===> qj xp vlvwhpd gh yl}lqkdqêd qr frqmxqwr gh qöv Vgr judir h F d frohêær gh vxfrqmxqwrv gh qöv irupdgrv shodv glihuhqwhv foltxhv

hvwdehohflgdv shor vlvwhpd gh yl}lqkdqfd Y1 Xp srwhqfldo gh�qlgr hp F ì xpd

frohêær gh ixqêøhv uhdlv wdlv txh fdgd xpd ghodv ghshqgh dshqdv grv ydoruhv gh �

hp xpd foltxh1

H{lvwh xpd lpsruwdqwh vxsrvlêær qr whruhpd gh Kdpphuvoh| h Fol�rug txh

dsduhqwhphqwh dlqgd qær irl uhod{dgd1 Hod ì fkdpdgd gh frqglêær gh srvlwlylgdgh=

Page 67: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

95 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

vh � @ +�4> = = = > �q, ì xpd frq�jxudêær wdo txh d glvwulexlêær pdujlqdo i+�l, A 3

sdud wrgr l hqwær i+�, A 3 wdpeìp1 Lvwr ì/ vh fdgd xp grv ydoruhv �4> = = = > �q

srgh rfruuhu lqglylgxdophqwh qrv uhvshfwlyrv qöv 4> ===> q hqwær hohv srghp rfruuhu

mxqwrv vlpxowdqhdphqwh1

Whruhpd gh Kdpphuvoh| h Fol�rug= Vhmd Y @ iCl> l @ 4> ===> qj xp vlv0

whpd gh yl}lqkdqêd qr frqmxqwr gh qöv V gr judir h F d frohêær gh foltxhv hp

Y 1 Hqwær xpd glvwulexlêær frqmxqwd i+�, vdwlvid}hqgr d frqglêær gh srvlwlylgdgh

srvvxl d sursulhgdgh Pdunryldqd +716, hp Y vh h vö vh hvwd glvwulexlêær frqmxqwd

srgh vhu hvfulwd frpr

i+�, 2 h{s

#[F5F

XF+�,

$@ h{s

#[F5F

XF+�F,

$+717,

D frqvwdqwh gh lqwhjudêær gd glvwulexlêær ì fkdpdgd gh ixqêær gh sduwlêær/ xp

qrph klvwöulfr ylqgr gd iðvlfd hvwdwðvwlfd1 Revhuyh txh dv ixqêøhv XF+�, srghp

vhu gh�qlgdv gh irupd duelwuäuld1 Sru h{hpsor/ XF+�, srgh vhu lghqwlfdphqwh qxod

sdud yäulrv wlsrv gh foltxhv uhgx}lqgr d vrpdS

F5F XF+�, d dshqdv dojxqv wlsrv

gh foltxhv1

D suryd ghvwh whruhpd qxqfd irl dsuhvhqwdgd sru Kdpphuvoh| h Fol�rug pdv

vlp/ dojxqv dqrv ghsrlv gr uhvxowdgr vhu frqkhflgr/ sru Ehvdj +4<:7, qxp duwljr

ixqgdphqwdo hp hvwdwðvwlfd hvsdfldo1 Hperud d suryd ghvwh whruhpd qær idêd xvr

gh wìfqlfdv pdwhpäwlfdv vr�vwlfdgdv h srvvd vhu hqwhqglgd sru txdotxhu hvwxgdqwh

frp frqkhflphqwr eävlfr gh suredelolgdghv/ qær ydprv dsuhvhqwä0od srlv hod ì xp

wdqwr orqjd h qær wud} frqkhflphqwrv dglflrqdlv txh srvvdp vhu ýwhlv qd dqäolvh

gh gdgrv1 R ohlwru lqwhuhvvdgr ghyh frqvxowdu Ehvdj +4<:7,1

Ydprv lqwurgx}lu pdlv xpd qrwdêær dx{loldu sdud vlpsol�fdu dv iöupxodv gdtxl

sud iuhqwh= l � m vljql�fd txh dv äuhdv l h m vær yl}lqkdv1

H{dpsoh 7 Vxsrqkd txh r pdsd vhmd irupdgr sru xpd judgh uhjxodu frpr xp

wdexohlur gh {dguh}1 Fdgd qö/ rx äuhd/ l srvvxl xpd yduläyho dohdwöuld �l1 D

yl}lqkdqfd ì dtxhod gr prylphqwr gr shær qr mrjr gh {dguh}1 Hqwær/ gh dfrugr

frp r Whruhpd gh Kdpphuvoh| h Fol�rug/ xpd glvwulexlêær pdunryldqd qhvwh

Page 68: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7161 SULRULV HVSDFLDOPHQWH HVWUXWXUDGDV 96

pdsd whp gh vhu gd irupd

i+�4> = = = > �q, 2 h{s

3C[l

jl+�l, .[l�m

kl>m+�l> �m,

4DLvwr ì/ r orjdulwpr gd ghqvlgdgh ì sursruflrqdo ã vrpd gh whuprv txh ghshqghp

gh fdgd äuhd lqglylgxdophqwh h gh sduhv gh äuhdv yl}lqkdv1 Revhuyh txh/ vh d

hvwuxwxud gh yl}lqkdqfd ì d gr prylphqwr gr uhl/ d glvwulexlêær dflpd dlqgd gh�qh

xp fdpsr dohdwöulr pdunryldqr srlv/ qhvwh fdvr/ dv ixqêøhv XF+�, edvhdgdv hp

foltxhv irupdgdv sru wulsodv +�l> �m > �n, vhuldp lghqwlfdphqwh qxodv1

H{dpsoh 8 R prghor gh Lvlqj ì xp prghor frpxp hp iðvlfd hvwdwðvwlfd h ì

gh�qlgr vreuh xpd hvwuxwxud hvsdfldo qd irupd gh xpd judgh uhjxodu +fkdpgd gh

uhwlfxodgr/ hp iðvlfd hvwdwðvwlfd,1 Fdgd qö/ rx äuhd/ l srvvxl xpd yduläyho dohdwöuld

elqäuld �l dvvxplqgr ydoruhv 4 rx �4 h sruwdqwr d glvwulexlêær gh suredelolgdgh

ghyh vhu glvfuhwd1 Qxpd judgh uhjxodu frp q qöv/ h{lvwhp 5q frqijxudêøhv rx

pdsdv srvvðyhlv1 Hvwh qýphur ì h{wuhpdphqwh judqgh phvpr sdud q prghudgd0

phqwh judqghv1 Qxpd judgh ;� ; frp q @ 97 äuhdv/ whuðdprv gd rughp gh 4353

frq�jxudêøhv srvvðyhlv1 Hvwh judqgh qýphur gh frq�jxudêøhv ì xpd gdv sulqflsdlv

gl�fxogdghv sdud r fäofxor gd frqvwdqwh gh lqwhjudêær1

Sdud hvwh prghor/ d glvwulexlêær gh suredelolgdgh ì

i+�4> = = = > �q, 2 h{s

3Ce[l�m

�l�m

4D +718,

Sru fdxvd gd qdwxuh}d elqäuld frpr 4 rx �4gdv yduläyhlv/ revhuyh txhSl�m

�l�m @

V4�V5 rqgh V4 ì d vrpd grv sduhv gh äuhdv yl}lqkdv l h m wdlv txh �l @ �m h V5 ì

d vrpd grv sduhv gh äuhdv yl}lqkdv l h m wdlv txh �l 9@ �m1 Frpr r qýphur wrwdo Q

gh sduhv gh äuhdv yl}lqkdv ì �{r/ whprv V5 @ Q � V4 h sruwdqwr srgh0vh hvfuhyhu

i+�4> = = = > �q, 2 h{s +eV4,1 Lvwr ì/ d glvwulexlêær gh suredelolgdgh ghshqgh dshqdv

gr qýphur gh sduhv gh äuhdv yl}lqkdv frp ydoruhv ljxdlv txh/ sruwdqwr/ ì xpd

hvwdwðvwlfd vx�flhqwh sdud r sduåphwur e1 Ghshqghqgr gr ydoru gh e/ frq�jxudêøhv

frp frqjorphudgrv gh ydoruhv ljxdlv srghp vhu hvwlpxodgrv uhfhehqgr pdlv pdvvd

gh suredelolgdgh +fdvr gh e A 3, rx/ dowhuqdwlydphqwh/ ghvhvwlpxodgrv +vh e ? 3,1

Page 69: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

97 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

Txdqgr e @ 3/ d suredelolgdgh gh wrgdv dv frq�jxudêøhv ì d phvpd h dv ydoruhv

qdv glihuhqwhv äuhdv vær lqghshqghqwhv1

D Iljxud 715 prvwud txdwur uhdol}dêøhv dohdwöuldv gh xp prghor gh Lvlqj1 Dv

frq�jxudêøhv irudp jhudgdv d sduwlu gd glvwulexlêær gh suredelolgdgh gr prghor gh

Lvlqj frp sduåphwur e srvlwlyr h yduldqgr sdud h{lelu r vhx hihlwr gh hvwlpxodgru

gd rfruuíqfld gh frqjorphudgrv hvsdfldlv1 Qhvwh pdsd uhjxodu frp q @ 89 � 89/

d äuhd l ì suhwd rx eudqfd gh dfrugr frp r ydoru 4 rx �4 gd yduläyho dohdwöuld �l1R ydoru gr sduåphwur e ì= +D, e @ 3=4/ +E, e @ 3=78/ +F, e @ 3=7:/ +G, e @ 7=31

H{dpsoh : R prghor gh Srwwv ì xp prghor suredeloðvwlfr frpxp hp dqäolvh gh

lpdjhqv txh hqyroyhp pdlv gh gxdv fruhv rx yäuldv wrqdolgdghv gh xpd phvpd

fru frpr/ sru h{hpsor/ rv yäulrv wrqv gh flq}d qxpd lpdjhp hp suhwr h eudqfr1

Qrydphqwh frqvlghuh xpd judgh uhjxodu rqgh fdgd qö/ rx äuhd/ l srvvxl xpd

yduläyho dohdwöuld elqäuld �l dvvxplqgr ydoruhv fdwhjöulfrv 4>5> ===> n uhsuhvhqwdqgr

glihuhqwhv fruhv +rx glihuhqwhv wrqv gh xpd fru,1 Dlqgd xwlol}dqgr d yl}lqkdqfd gh

shær gr mrjr gh {dguh}/ r prghor gh Srwwv gh�qh d glvwulexlêær gh suredelolgdgh

gdgd sru

i+�4> = = = > �q, 2 h{s

3Ce[l�m

L�l@�m

4DH{dpsoh ; Yrowdqgr ã judgh uhjxodu rqgh dv yduläyhlv �l vær elqäuldv frp ydo0

ruhv �4 rx 4/ xp prghor xp srxfr pdlv jhudo txh r prghor gh Lvlqj ì dtxhoh rqgh

d ixqêær gh suredelolgdgh ì gdgd sru

i+�4> = = = > �q, 2 h{s

3C[l

dl�l .4

W

[l�m

elm�l> �m

4Drqgh dl vær frqvwdqwhv duelwuäuldv/ rv elm vær ljxdlv d 4 rx �4 h W ì xpd

frqvwdqwh srvlwlyd fkdpdgd gh whpshudwxud1 R hihlwr gh elm ì hvwlpxodu rx qær d

rfruuíqfld gh yl}lqkrv frp fruhv ljxdlv1 Revhuyh txh hvwh hihlwr srgh ghshqghu gr

sdu hvsfð�fr +l> m, gh yl}lqkrv txh hvwä hp txhvwær1 Frp elm @ 4/ frq�jxudêøhv

frp �l @ �m qr sdu gh yl}lqkrv +l> m, vær hqfrudmdgdv d rfruuhu hqtxdqwr txh/ frp

elm @ �4/ r sdu gh äuhdv +l> m, whqgh d prvwudu frq�jxudêøhv frp �l 9@ �m1 R ydoru

Page 70: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7161 SULRULV HVSDFLDOPHQWH HVWUXWXUDGDV 98

H{dpsoh 9

Iljxud 715= Txdwur frq�jxudêøhv dohdwöuldv jhudgdv d sduwlu gd glvwulexlêær gh

suredelolgdgh gr prghor gh Lvlqj qxp pdsd uhjxodu frp q @ 89 � 891 Äuhd l ì

suhwd rx eudqfd gh dfrugr frp r ydoru 4 rx �4 gd yduläyho dohdwöuld �l1 R ydoru

gr sduåphwur e +srvlwlyr, dxphqwd dr orqjr gdv lpdjhqv hvwlpxodqgr d rfruuíqfld

gh frqjorphudgrv gh ydoruhv ljxdlv= +D, e @ 3=4/ +E, e @ 3=78/ +F, e @ 3=7:/ +G,

e @ 7=31 +H{wudðgr gh Zulqnohu/ 4<<9,

Page 71: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

99 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

Iljxud 716= Prghor gh Lvlqj frp whpshudwxud W txh pxgd d phglgd txh sdvvdprv

gh +D, sdud +E,1 +H{wudðgr gh Zulqnohu/ 4<<9,

gd whpshudwxud W frqwurod r judx ghvwh �hvwðpxor� txh ì gdgr qd jhudêær gdv

frq�jxudêøhv dohdwöuldv/ txdqwr phqru d whpshudwxud/ pdlru r hihlwr gr vlqdo gh

elm1

H{dpsoh < D Iljxud 716 prvwud txdwur uhdol}dêøhv dohdwöuldv gr prghor dflpd

frp dl @ 3 sdud wrgr l h frp wrgrv rv elm @ 4 h{fhwr dojxqv txh srvvxhp elm @ �41Rv sduhv gh yl}lqkrv rqgh elm @ �4 vær dtxhohv txh gh�qhp dv olqkdv gr frqwruqr

gd idfh/ rokrv h erfd gr urvwr txh hvwä fodudphqwh vxjhulgr qd lpdjhq +G,1 R ydoru

gh W ydl glplqxlqgr d phglgd txh sdvvdprv gd lpdjhp hp +D, sdud d lpdjhp

hp +G,1

Page 72: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7161 SULRULV HVSDFLDOPHQWH HVWUXWXUDGDV 9:

Ì frpxp hvshfl�fdu rv prghorv hvsdfldlv dwudyìv gr vlvwhpd gh glvwulexlêøhv

frqglflrqdlv i+�lm��l, @ i +�lm i�m wdlv txh m 5 Clj, vdwlvid}hqgr d sursulhgdgh

pdunryldqd 716 dr lqyìv gh hvshfl�fdu d glvwulexlêær frqmxqwd i+�4> = = = > �q,1 Hvwdv

glvwulexlêøhv h{suhvvdp r frpsruwdphqwr orfdo gh fdgd äuhd frqglflrqdgr qxpd

frq�jxudêær gh vhxv yl}lqkrv dr lqyìv gh hvshfl�fdu d glvwulexlêær vlpxowåqhd gd

frq�jxudêær gh wrgr r pdsd1 H{suhvvdu r frpsruwdphqwr orfdo frqglflrqdo ì

pdlv vlpsohv h iäflo gh vhu ihlwr1 Dvvlp/ r uhvxowdgr gr Whruhpd gh Kdpphuvoh| h

Fol�rug dsuhvhqwdgr dedl{r ì gh ghprvwudêær wulyldo pdv edvwdqwh ýwlo h sru lvwr

uhfheh r qrph gh fruroäulr qhvwh wh{wr1

Fruroäulr= hmd Y @ iCl> l @ 4> ===> qj xp vlvwhpd gh yl}lqkdqêd qr frqmxqwr

gh qöv V gr judir h F d frohêær gh foltxhv hp Y 1 Hqwær xpd glvwulexlêær frqmxq0

wd i+�, vdwlvid}hqgr d frqglêær gh srvlwlylgdgh srvvxl d sursulhgdgh Pdunryldqd

+716, srvvxl glvwulexlêær gh �l frqglflrqdgd qrv ydoruhv gh �� l gdgd sru

i+�lm��l, @ i +�lm i�m wdlv txh m 5 Clj, 2 h{s

#[Fl5F

XFl+�Fl

,

$+719,

rqgh Fl vær dv foltxhv txh hqyroyhp d äuhd l1

Sdud surydu r uhvxowdgr/ xvh d gh�qlêær gh glvwulexlêær frqglflrqdo sduwlqgr

gd h{suhvvær frqmxqwd 717 gdgd qr Whruhpd gh Kdpphuvoh| h Fol�rug1 R fruroäulr

gä xpd irupd h{wuhpdphqwh vlpsohv gh rewhu d glvwulexlêær frqglflrqdo d sduwlu

gd glvwulexlêær frqmxqwd= edvwd pdqwhu dshqdv rv whuprv gd vrpd hp 717 txh

hqyroyhp r ðqglfh l1 Sru h{hpsor/ qr fdvr gr prghor gh Lvlqj 718 d glvwulexlêær

frqglflrqdo vhuä ljxdo d

i+�lm�� l, @ i+�lm i�m wdlv txh m 5 Clj, 2 h{s

3Ce[m5Cl

�l�m

4D 2 h{s +eVl, +71:,

rqgh Vl ì r qýphur gh äuhdv yl}lqkdv ä äuhd l txh srvvxhp r phvpr ydoru +4 rx

�4, txh hod1

71616 Sulrulv hvsdfldlv sdud gdgrv frp glvwulexlêær qrupdo

Rv hihlwrv dohdwöulrv hvsdfldophqwh hvwuxwxudgrv gd sulrul gh xpprghor klhuäutxlfr

ed|hvldqr vær frqwðqxrv h dvvlp ì lpsruwdqwh frqvlghudu rxwurv prghorv doìp grv

Page 73: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

9; FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

prghorv sdud yduläyhlv dohdwöuldv glvfuhwdv dsuhvhqwdgrv dflpd1 R prghor pdlv

srsxodu ì dtxhoh hp txh d glvwulexlêær frqmxqwd ì xpd glvwulexlêær qrupdo pxo0

wlyduldgd1 Dvvlp/ d txhvwær ì vdehu txdqgr xpd glvwulexlêær qrpdo pxowlyduldgd

srgh ylu d vhu xp fdpsr dohdwöulr gh Pdunry1

Vxsrqkd txh � srvvxl xpd glvwulexlêær qrupdo pxowlyduldgd frp pìgld 3q h

pdwul} gh frydulåqfld �5� rqgh 3q ì xp yhwru q � 4 gh }hurv/ �5� A 3 frqwurod

d yduldelolgdgh grv �l*v h ì xpd pdwul} q � q vlpìwulfd h gh�qlgd srvlwlyd1

Vhmd T @ �4 d pdwul} gh suhflvær gh �1 Ì xp uhvxowdgr sdguær gh qrupdo

pxowlyduldgd d rewhqêær gd ghqvlgdgh frqglflrqdo gh �l gdgrv rv ghpdlv ydoruhv

+�4> = = = > �l�4> �l.4> = = = > �n, @ �� l=

i+�lm�� l, � Q

3C q[m@4

Zlm�m> �5�Yll

4D +71;,

rqgh Zll @ 3>Zlm @ �Tlm@Tll h Yll @ T�4ll 1 Hvwh prghor ì fkdpdgr gh prghor

dxwrqrupdo +Ehvdj/ 4<:7,1 Revhuyh txh r ydoru hvshudgr gh �l ì xpd vrpd srq0

ghudgd grv ghpdlv ydoruhv hp �� l1 Frpr ì vlpìwulfd/ T/ txh ì vxd lqyhuvd/

wdpeìp ì vlpìwulfd1 Dvvlp/ frqfoxlprv txh TllZlm @ �Tlm @ �Tml @ TmmZml h/

frprYll @ T�4ll / whprv

ZlmGmm @ZmlGll +71<,

Hvshfl�fdu d pdwul} gh shvrvZ h dv ydulåqfldv frqglflrqdlv Yll ì htxlydohqwh d

hvshfl�fdu d pdwul} gh suhflværT mä txh hodv vær uhodflrqdgdv dwudyìv gd h{suhvvær

T @Y�4 +L �Z, +7143,

rqgh Y ì xpd pdwul} gldjrqdo frqwhqgr rv hohphqwrv Yll> l @ 4> ===> q1

Gdgd xpd hvwuxwxud jhrjuä�fd gh�qlqgr xp vlvwhpd gh yl}lqkdqfd

Y @ iCl> l @ 4> ===> qj

h vxdv foltxhv dvvrfldgdv/ d shujxqwd gh lqwhuhvvh ì d vhjxlqwh= txdqgr xpd glv0

wulexlêær qrupdo pxowlyduldgd/ txh qhfhvvduldphqwh srvvxl dv glvwulexlêøhv frqgl0

flrqdlv uhsuhvhqwdgdv hp 71;/ srvvxl d sursulhgdgh pdunryldqdB Dr lqyìv gh

Page 74: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7161 SULRULV HVSDFLDOPHQWH HVWUXWXUDGDV 9<

yhul�fdu vh d glvwulexlêær frqmxqwd vdwlvid} d irupd 717 h{lelgd qr Whruhpd gh

Kdpphuvoh| h Fol�rug/ ydprv yhul�fdu d irupd gh vxdv glvwulexlêøhv frqglflrqdlv1

Hvwd glvwulexlêær frqglflrqdo suhflvd vhu gr wlsr 719 dsuhvhqwdgr shor Fruroäulr1

Lvwr ì/ rv shvrv Zlm suhflvdp vhu frpsdwðyhlv frp d hvwuxwxud gh yl}lqkdqfd hv0

froklgd h vxdv foltxhv dvvrfldgdv1 Hp sduwlfxodu/ vh n @5 Cl/ hqwær �n qær srgh

dsduhfhu qd ghqvlgdgh 71; h sruwdqwr Zln @ 3 r txh lpsolfd txh Tln @ 31 Doìp

glvwr/ frpr T @ �4 ì vlpìwulfd/ sdud h{lvwlu xpd hvwuxxwud pdunryldqd qrupdo

d hvwuxwxud gh yl}lqkdqfd suhflvd vhu vlpìwulfd= vh l ì yl}lqkr gh m hqwær m ghyh

vhu yl}lqkr gh l1

Dvvlp/ ghyh0vh hvfrokhu Yll A 3 h Zlm uhvshlwdqgr d frqglêær gh vlphwuld 71< h

}hudqgr rv shvrvZlm grv sduhv gh äuhdv txh qær vær yl}lqkdv pdv jdudqwlqgr txh d

pdwul} T gh�qlgd hp 7143 h{lvwd1 Lqihol}phqwh/ vdwlvid}hu 719 qær ì vx�flhqwh sdud

txh d glvwulexlêær frqmxqwd uhdophqwh h{lvwd srlv srgh qær h{lvwlu xpd pdwul} gh

suhflvær T gh�qlgd srvlwlyd1

Xp prghor gh fdpsrv gh Pdunry pxlwr srsxodu sdud sulrulv hvsdfldlv ì r

fkdpdgr prghor lqwuðqvhfr dxwruhjuhvvlyr frqglflrqdo sru Ehvdj hw do1 +4<<4, h

gdgr sru

+�lm�m> m 9@ l, � Q

��l>

�5�ql

�+7144,

rqgh ql @ & Cl ì r q�xphur gh yl}lqkrv gh l hpl ì d pìgld dulwpìwlfd gr frqmxqwr

gh yl}lqkrv i�m > m 5 Clj1 Frpsdudqgr frp d h{suhvvær hp 71; yhul�fdprv txh

Zlm @ 4@ql sdud äuhdv yl}lqkdv h Zlm @ 3/ fdvr frqwuäulr h Yll @ 4@ql1 Hvwd

hvshfl�fdêær vlpsohv h qdwxudo qær ohyd d xpd pdwul} T gh�qlgd srvlwlyd1 Sdud

yhul�fdu lvwr/ edvwd qrwdu txh dv vrpdv gdv olqkdv gh L�Z vær wrgdv lghqwlfd0

phqwh ljxdlv d }hur mä txh d l0ìvlpd olqkd srvvxl xpd ýqlfd hqwudgd ljxdo d 4 h

dv q � 4 uhvwdqwhv ljxdlv d �4@ql1 Dvvlp/ T qær whp srvwr frpsohwr h qær ì

lqyhuwðyho1

D irupd gh xpd glvwulexlêær frqmxqwd txh lpsolfduld qdv glvwulexlêøhv frqgl0

flrqdlv hp 71; ì gdgd sru

i+�4> = = = > �q, 2 h{s

3C� 4

5�5�

[l�m

+�l � �m,5

4D +7145,

Page 75: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

:3 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

Ilfd pdlv fodur djrud txh d glvwulexlêær frqmxqwd +7145, ì xpd glvwulexlêær

lpsuösuld srlv vhx odgr gluhlwr ì lqyduldqwh sru wudqvodêær gh � sru phlr gh xpd

phvpd frqvwdqwh f dglflrqdgd d wrgrv rv vhxv hohphqwrv1 Lvwr ì/ i+�4> = = = > �q, @

i+�4 � f> = = = > �q � f, h sruwdqwr d lqwhjudo hp Uq gd ixqêær 7145 qær ì �qlwd1 Hod

srgh vhu wudqvirupdgd qxpd sulrul suösuld dglflrqdqgr dojxpd uhvwulêær olqhdu

txh rv sduåphwurv ghyhuldp vdwlvid}hu1

Hperud qær vhmd qhfhvväulr wudqvirupdu 7145 qxpd sulrul suösuld sdud rewhu

xpd glvwulexlêær suösuld/ hvwh surfhglphqwr/ fkdpdgr gh fhqwhulqj rq wkh | sru

Ehvdj hw do1 +4<<8,/ gä drv dojrulwprv gh Prqwh Fduor yld Fdghldv gh Pdunry

xp ghvhpshqkr phokru1 Ì xvxdo lpsru d uhvwulêærS

l �l @ 3 hperud rxwudv

rsêøhv srvvdp vhu pdlv vdwlvidwöuldv ghshqghqgr gr sureohpd1 Yhu Dvvxqêær h

Uhlv +5334, sdud ghwdokhv1

H{lvwh rxwud srvvlelolgdgh sdud frqwruqdu r sureohpd gh rewhu xpd glvwulexlêær

suösuld pdqwhqgr xpd hvwuxwxud gh glvwulexlêøhv frqglflrqdlv orfdlv wær vlpsohv

txdqwr 7145= dgrwdu xpd glvwulexlêær suösuld sdudp wdo txh d glvwulexlêær frqgl0

flrqdo H+�lm�m 9@l, @ ��l dqg � 5 +3> 4,1 Jhudophqwh/ frp hvwh sduåphwur dglflrqdo

vhqgr hvwlpdgr hqfrqwud0vh xpd srvwhulrul edvwdqwh frqfhqwudgd hp wruqr gd iurq0

whlud 41 Lvwr ohyd Ehvdj hw do1 +4<<4, h Ehvdj h Nrrshuehuj +4<<8,1

Rxwurv dxwruhv frqvlghudp rxwudv dowhuqdwlydv gh gh�qlêær grv shvrvZlm sdud

jdudqwlu xpd glvwulexlêær suösuld sdud p +Fuhvvlh h Fkdq/ 4<;<,1

D vlwxdêær dwxdo ì gh judqgh srsxodulgdgh gr prghor lqwurgx}lgr sru Ehvdj hw

do1 +4<<4, gh sulrulv hvsdfldlv gh�qlgdv frqglflrqdophqwh frpr fdpsrv dohdwöulrv

gh Pdunry frpr h{solfdprv dflpd1 Hqwuhwdqwr frphfdp d vxujlu lpsruwdqwhv

shvtxlvdgruhv/ frpr Shwhu Gljjoh/ frqvwuxlqgr xp frqmxqwr gh prghorv xvdqgr d

derugdjhp jhrhvwdwðvwlfd1 Txdo ghvwdv gxdv derugdjhqv ì phokru/ d gh jhrhvwdwðv0

wlfd rx dtxhod edvhdgd hp prghorv gdv glvwulexlêøhv frqglflrqdlv/ ì xp dvvxqwr

gh shvtxlvd sdud rv suö{lprv dqrv h ghyhuä vhu uhvsrqglgd sru uhvxowdgrv whöulfrv

h frpsdudêøhv hpsðulfdv1

Page 76: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7171 LPSOHPHQWDÊÆR :4

717 Lpsohphqwdêær

Rewhqgr0vh d srvwhulrul d phqrv gh xpd frqvwdqwh frpr hp 715/ jhudprv dprvwudv

dohdwöuldv ghshqghqwhv gh # @ +#4> ===> #q,/ doìp grv rxwurv sduåphwurv h klshu0

sduåphwurv/ srvvxlqgr xpd glvwulexlêær dsur{lpdgdphqwh ljxdo ã glvwulexlêær

frqmxqwd1 R pìwrgr gh jhudêær ì jhqìulfr/ qær srvvxl qdgd hvshfð�fr sdud r frq0

wh{wr hvsdfldo/ h ì edvhdgr qrv dojrulwprv gh Prqwh Fduor yld Fdghld gh Pdunry

+PFPF,1 H{lvwhp pxlwrv olyurv h duwljrv gh uhylvær ghvwh dvvxqwr glvsrqðyhlv kr0

mh hp gld/ qrv pdlv glyhuvrv qðyhlv/ h ydprv rplwlu dtxl txdotxhu ghwdokdphqwr

vreuh hohv1 Rv pìwrgrv sdud lqihuíqfld ed|hvldqd hvwær lpsohphqwdgrv qr vriw0

zduh hvwdwðvwlfr ZlqEXJV +Vslhjhokdowhu hw do1/ 4<<9,/ pxlwr iäflo gh vhu xvdgr/ h

txh lqfoxl ixqêøhv hvshfð�fdv sdud dmxvwdu dv sulrulv dxwruhjuhvvlydv frqglflrqdlv

glvfxwlgdv dqwhulruphqwh1

Sdud qrvvr sureohpd/ edvwd vdehu txh/ dsöv xp shuðrgr lqlfldo gh frqyhujíq0

fld gd fdghld sdud d glvwulexlêær hvwdflrqäuld +txh ì d glvwulexlêær d srvwhulrul,/

frohwdprv rv ydoruhv jhudgrv sdud frqvwlwxlu d dprvwud vlpxodgd1 D sduwlu ghvwd

dprvwud/ wrpdgd wær judqgh txdqwr ghvhmdgr/ srgh0vh fdofxodu txdotxhu fdudfwhuðv0

wlfd gd glvwulexlêær frqmxqwd d srvwhulrul grv sduåphwurv h klshusduåphwurv1 Hp

sduwlfxodu/ dv pìgldv/ ydulåqfldv h shufhqwlv gdv glvwulexlêøhv pdujlqdlv gh fdgd

sduåphwur srghp vhu fdofxodgdv idflophqwh1 Qr frqwh{wr gh pdsdv gh grhqêdv/

lvwr vljql�fd txh hvwlpdwlydv srqwxdlv +pìgldv d srvwhulrul, h lqwhuydorv gh fuhg0

lelolgdgh srghp vhu iruqhflgrv sdud rv ulvfrv uhodwlyrv #l xwlol}dqgr pìwrgrv gh

prphqwrv1

Vxsrqkd txh #+4,> ===>#

+E, ì xpd dprvwud dohdwöuld jhudgd sru PFPF frp E

edvwdqwh judqgh gr yhwru gh lqwhuhvvh# +hvwh yhwru srgh lqfoxlu rv klshusduåphwurv

wdpeìp,1 Vxsrqkd txh d fdudfwhuðvwlfd gh lqwhuhvvh ì xp ixqflrqdo � @ W +I ,

txdotxhu gd glvwulexlêær frqmxqwd d srvwhulrul I 1 Xpd hvwlpdwlyd srqwxdo gh � ì

rewlgd shor pìwrgr gh prphqwrv dvvxplqgr txh E ì edvwdqwh judqgh= e� @ W +fIE,rqgh fIE ì d ixqêær gh glvwulexlêær dfxpxodgd hpsðulfd edvhdgd hp #+4,> ===>#+E,1

Dvvlp/ d hvwlpdwlyd gd pìgld d srvwhulrul � gr ulvfr uhodwlyr #l gd äuhd l ì gdgd

shod pìgld dulwpìwlfd grv ydoruhv vlpxodgrv #+4,l > ====> #

+E,l 1

Page 77: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

:5 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

Srghprv wdpeìp rewhu dv glvwulexlêøhv d srvwhulrul gh txdqwlgdghv ghulydgdv

txh vhuldp pxlwr gliðfhlv gh vhuhp hvwxgdgdv dqwhv gr dgyhqwr gr PFPF1 Sru

h{hpsor/ srghprv fdofxodu d suredelolgdgh gh txh r ulvfr uhodwlyr gdv äuhdv 6>;

h 4:/ vhohflrqdgdv sru dojxp prwlyr/ srvvxdp ulvfr uhodwlyr pdlru txh 51 Lvwr

ì/ srghprv fdofxodu S +#6 A 5> #; A 5> #4: A 5m|4> ===> |q,1 Hvwh fäofxor ì vlpsohv0

phqwh d iuhtxíqfld uhodwlyd gd rfruuíqfld gr hyhqwr ^#6 A 5> #; A 5> #4: A 5` qdv

dprvwudv vlpxodgdv1

Dvvlp/ d lqihuíqfld d srvwhulrul edvhdgd qdv dprvwudv vlpxodgdv shor surfhg0

lphqwr PFPF vhjxh pìwrgrv vlpsohv frpr r pìwrgr gh prphqwrv mxvwl�fdqgr

vxd ydolgdgh dwudyìv gh dujxphqwrv iuhtxhqwlvwdv wdlv frpr d Ohl grv Judqghv

Qýphurv1 Qær ghl{d gh vhu fxulrvr revhuydu hvwh dvshfwr hfxpíqlfr gd lqihuíqfld

ed|hvldqd prghuqd1

718 H{hpsor

Qhvwd vhêær/ ydprv dsuhvhqwdu xp h{hpsor ghwdokdgr hqyroyhqgr gdgrv gh pru0

wdolgdgh lqidqwlo qrv 977 pxqlfðslrv gh Vær Sdxor hp 4<<: +h{foxlqgr r pxqlfðslr

gh Lokdehod txh qær srvvxl yl}lqkrv qdwxudlv,1 D wd{d gh pruwdolgdgh lqidqwlo qr

hvwdgr frpr xp wrgr irl gh 5418< sru plo qdvflgrv ylyrv1 Lvwr ì/ dsur{lpdgdphqwh

5( gdv fuldqfdv qdvflgdv ylydv hp Vær Sdxor pruuhp dqwhv gh frpsohwdu xp dqr

gh lgdgh1 Qr hqwdqwr/ hvwd pruwdolgdgh qær dihwd d wrgrv gh pdqhlud xqliruph h/

hp sduwlfxodu/ hod srvvxl xpd jhrjud�d pxlwr ehp gh�qlgd/ frpr prvwuduhprv

dtxl1

D wd{d euxwd gr pxqlfðslr l/ fdofxodgd frpr ul @ |l@Ql/ srvvxl xpd glv0

wulexlêær pxlwr dvvlpìwulfd frqiruph prvwud d Wdehod 714 frp rv txdqwlv pdlv

uhohydqwhv1 Dvvlp/ 4( grv pxqlfðslrv dsuhvhqwdydp xpd hvwlpdwlyd gd wd{d txh

hud shor phqrv 618 yh}hv pdlru txh d pìgld gr hvwdgr/ xpd vlwxdêær edvwdqwh

judyh1 Qr hqwdqwr/ frpr yhuhprv d vhjxl/ d pdlru sduwh ghvwd yduldêær qær srgh

vhu dwulexðgd d xpd yduldêær gr ulvfr vxemdfhqwh1

Frqvlghudprv wuív prghorv ed|hvldqrv txh vh glvwlqjxldp shorv hihlwrv dohdwöulrv

frqvlghudgrv qd prghodjhp gr ulvfr1 Dgrwdqgr d qrwdêær gd ghfrpsrvlêær gr +orj

Page 78: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7181 H[HPSOR :6

43( 58( 83( :8( <3( <8( <<( pä{lpr

3 46173 53174 541;9 7317: 7:195 :8139 43313

Wdehod 714= Wdehod frp hvwdwlwlfdv ghvfulwlydv gdv wd{dv euxwdv sru pxqlfðslr1

gr, ulvfr uhodwlyr/ orj#l @ �l @ !l . �l/ hp xp frpsrqhqwh dohdwöulr sxur/ !l/ h

xp frpsrqhqwh hvsdfldo/ !l/ rv prghorv vær rv vhjxlqwhv=

� P4= �l @ !l/ prghor dshqdv frp hihlwrv dohdwöulrv sxurv1

� P5= �l @ �l/ prghor dshqdv frp hihlwrv hvsdfldlv prghodgrv d sulrul frpr

xp fdpsr gh Pdunry1

� P6= �l @ !l . �l/ prghor frp dperv rv hihlwrv1

Xvdprv r surjudpd ZlqEXJV sdud urgdu rv prghorv h r fögljr qhfhvväulr

sdud r whufhlur prghor ì r vhjxlqwh=

prgho

~

e^4=duhdv` �fdu1qrupdo+dgm^`/ zhljkwv^`/ qxp^`/ wdxe,

e1phdq ?0 phdq+e^`,

iru +l lq 4 = duhdv, ~

R^l` �gsrlv+px^l`,

orj+px^l`, ?0 orj+QY^l`, . doskd3 . j^l` . e^l`

wd{dkdw^l` ?0 4333 - h{s+doskd3 . j^l` . e^l`,

j^l` �gqrup+3/ wdxj,

doskd3 �giodw+,

wdxe �gjdppd+uvwdu/ gvwdu,

vljpde ?0 4 2 vtuw+wdxe,

wdxj �gjdppd+31334/31334,

vljpdj ?0 4 2 vtuw+wdxj,

Page 79: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

:7 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

Rv ydoruhv lqlfldlv xvdgrv sdud rv hihlwrv dohdwöulrv vær lgíqwlfrv h ljxdlv d

}hur1 Sdud rv klshusduåphwurv irudp xvdgrv ydoruhv ljxdlv d 41 Rxwudv urgdgdv

frp ydoruhv edvwdqwh glihuhqwhv surgx}ludp hvvhqfldophqwh rv phvprv uhvxowdgrv

txh rv h{lelgrv d vhjxlu1 Dsöv urgdu r surfhglphqwr h yhul�fdu d frqyhujíqfld gdv

fdghldv/ rewhprv dv pìgldv d srvwhulrul gdv wd{dv hp fdgd äuhd h frpsdudprv rv

ydoruhv rewlgrv shorv glyhuvrv prghorv1

D Iljxud 717 prvwud hvwlpdwlydv gd ghqvlgdgh gdv wd{dv euxwdv h hvwlpdwlydv

ed|hvldqdv1 R juä�fr vxshulru ã hvtxhugd prvwud dv wd{dv euxwdv +olqkd wudfhmdgd,

h hvwlpdwlydv ed|hvldqdv edvhdgdv qd pìgld d srvwhulrul +olqkd vöolgd, xvdqgr r

prghor P41 Ì öeyld d frqwudêær h{wuhpd gdv hvwlpdwlydv hp gluhêær ã pìgld

joredo lqwurgx}lgd shor xvr gh hihlwrv dohdwöulrv sxurv1 R prghor P4 +olqkd wudfh0

mdgd, ì frqwudvwdgr frp r prghor P5 +olqkd vöolgd, qr juä�fr vxshulru ã gluhlwd1

R hihlwr gh lqwurgx}lu xp hihlwr dohdwöulr hvsdfldo ì ghvfrqwudlu xp srxfr dv hvwl0

pdwlydv hp uhodêær dr txh irl rewlgr shor prghor xvdqgr dshqdv hihlwrv dohdwöulrv1

D ud}ær glvwr ì r idwr gh txh/ ydoruhv pxlwr lqfhuwrv gd wd{d euxwd sdvvdp d vhu

frqwudðgrv hp gluhêær d xp ydoru orfdo dr lqyìv gh xp ydoru joredo1 D frpsdudêær

gr prghor P6 frp r prghor P4 +juä�fr dedl{r ã hvtxhugd, prvwud uhvxowdgrv

vhphokdqwhv ã frpsdudêær gh P5 frp P41 Lvwr ì frq�updgr qr juä�fr lqihulru ã

gluhlwd txh dsuhvhqwd dv hvwlpdwlydv gh ghqvlgdgh gr prghorv P5 h P6/ txh vær

yluwxdophqwh lgíqwlfdv1

D Iljxud 718 prvwud gldjudpdv gh glvshuvær gdv hvwlpdwlydv gdv wd{dv eux0

wdv h hvwlpdwlydv ed|hvldqdv +pìgldv d srvwhulrul,1 R juä�fr vxshulru ã hvtxhugd

prvwud dv wd{dv euxwdv +hl{r krul}rqwdo, h hvwlpdwlydv ed|hvldqdv edvhdgdv xvdqgr

r prghor P4 +hl{r yhuwlfdo,1 Fdgd pxqlfðslr ì xp srqwr gr juä�fr1 D hvfdod grv

grlv hl{rv ì d phvpd h lvwr shuplwh frqvwdwdu qrydphqwh d frqwudêær h{wuhpd gdv

hvwlpdwlydv ed|hvldqdv hp gluhêær ã pìgld joredo1 D ghvfrqfhqwudêær revhuydgd

dqwhulruphqwh srgh vhu qrwdgd qrv ghpdlv juä�frv= r juä�fr vxshulru ã gluhlwd

prvwud r prghor P5 +hl{r yhuwlfdo, yhuvxv dv wd{dv euxwdv h juä�fr lqihulru ã hv0

txhugd prvwud r prghor P6 yhuvxv dv wd{dv euxwdv/ xp juä�fr pxlwr sduhflgr frp

r dqwhulru1 R ýowlpr juä�fr prvwud frp xp srxfr pdlv gh ghwdokhv r frqwudvwh

hqwuh rv prghorv P4 h P51

Page 80: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7181 H[HPSOR :8

theta_i

dens

idad

e es

timad

a

0 20 40 60 80 100

0.0

0.05

0.10

0.15

theta_i

dens

idad

e es

timad

a20 30 40

0.0

0.05

0.10

0.15

theta_i

dens

idad

e es

timad

a

20 30 40

0.0

0.05

0.10

0.15

theta_i

dens

idad

e es

timad

a

20 30 40 50

0.0

0.05

0.10

0.15

Iljxud 717= Hvwlpdwlydv gd ghqvlgdgh gdv wd{dv euxwdv h hvwlpdwlydv ed|hvldqdv

xvdqgr d pìgld d srvwhulrul grv prghorv P4/ P5 h P61 Yhu wh{wr sdud ghwdokhv1

Page 81: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

:9 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

taxa usual de mortalidade infantil

Bay

es, s

o al

eato

rio

0 20 40 60 80 100

020

4060

8010

0

taxa usual de mortalidade infantil

Bay

es, s

o es

paci

al

0 20 40 60 80 100

020

4060

8010

0

taxa usual de mortalidade infantil

Bay

es, a

mbo

s os

efe

itos

0 20 40 60 80 100

020

4060

8010

0

Bayes, so aleatorio

Bay

es, s

o es

paci

al

20 30 40 50

2030

4050

Iljxud 718= Gldjudpdv gh glvshuvær gdv hvwlpdwlydv gdv wd{dv/ euxwd h ed|hvldqd

xvdqgr d pìgld d srvwhulrul grv prghorv P4/ P5 h P61 Yhu wh{wr sdud ghwdokhv1

Page 82: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7181 H[HPSOR ::

D Iljxud 715 prvwud xpd wdehod frp txdwur pdsdv gh hvwlpdwlydv gd pruwdol0

gdgh lqidqwlo hp Vær Sdxor hp 4<<: pdqwhqgr d phvpd hvfdod hp wrgrv rv pdsdv1

R sulphlur pdsd ì d wd{d euxwd/ r vhjxqgr ì r pdsd frp d pìgld d srvwhulrul

gr prghor P4 dshqdv frp rv hihlwrv dohdwöulrv sxurv/ r whufhlur ì r pdsd frp

d pìgld d srvwhulrul gr prghor P5 dshqdv frp rv hihlwrv dohdwöulrv hvsdfldlv/ r

txduwr ì r pdsd frp d pìgld d srvwhulrul gr prghor P6 frp dperv rv hihlwrv1

D dgrêær gh xpd hvfdod ýqlfd sdud wrgrv rv pdsdv prvwud hvsdfldophqwh r

hihlwr gh frqwudêær1 R pdsd gh wd{dv euxwdv vh sduhfh frp xpd frofkd gh uhwdokrv

gl�fxowdqgr xpd ylvær joredo pdlv qðwlgd1 Dshvdu glvwr/ srghprv qrwdu xp fhuwr

judglhqwh gh ghfuìvflpr gr ulvfr txdqgr sdvvdprv gr Vxghvwh sdud r Qrurhvwh

gr hvwdgr1 Hvwd sdguær �fd pxlwr pdlv qðwlgr qr vhjxqgr pdsd txh prvwud rv

uhvxowdgrv gr prghor P51 Qhvwh fdvr/ sduhfh kdyhu qd yhugdgh gxdv judqghv

uhjløhv/ xpd vhqgr xp foxvwhu gh dowr ulvfr qr h{wuhpr Vxghvwh1 R prghor P6

iruqhfh hvwlpdwlydv idflophqwh lqwhusuhwäyhlv h txh shuplwhp xpd lqwhusuhwdêær

pdlv vxwlo1 Sduhfh kdyhu xp ghfuìvflpr uäslgr pdv vlvwhpäwlfr d sduwlu gr h{wuhpr

vxghvwh/ dr lqyìv gh xp foxvwhu lqglvwlqwr gh dowr ulvfr qhvwd uhjlær1 R pdsd frp

dperv rv hihlwrv ì yluwxdophqwh lgíqwlfr dr dqwhulru/ frpr ì hvshudgr whqgr hp

ylvwd d dqäolvh dqwhulru1

D Iljxud 716 prvwud xpd wdehod frp rv phvprv txdwur pdsdv dqwhulruhv pdv

djrud frqvlghudqgr hvfdodv glihuhqwhv hp fdgd pdsd1 Lvwr shuplwh yhu frp pdlv

ghwdokhv d hvwuxwxud hvsdfldo txh dlqgd shuvlvwh phvpr dsöv d h{wuhpd frqwudêær

hp gluhêær ã pìgld hihwxdgd shorv pìwrgrv ed|hvldqrv1 Ilfd fodur txh r prghor

P4 qær lqgx} xpd iruwh fruuhodêær hvsdfldo hqwuh dv wd{dv hp frqwudvwh frp r

prghor P51 R prghor P6/ txh dsuhvhqwd xp frpsurplvvr hqwuh P4 h P5/ frp0

surplvvr gh�qlgr shorv shvrv gdgrv drv hihlwrv dohdwöulrv hvsdfldlv h qær hvsdfldlv/

prvwud txh rv gdgrv hqfrqwudp iruwh hylgíqfld d srvwhulrul sdud d suhvhqêd gh

xpd vxdyh pxgdqêd qrv ulvfrv/ ghfuhvfhqgr dr orqjr gr judglhqwh VH0QR/ frp

xp frqjorphudgr gh dowr ulvfr lghqwl�fdgr qr h{wuhpr Qruwh1

Txdqwr drv ydoruhv grv rxwurv sduåphwurv/ srghprv uhvxpl0orv qd wdehod dedl{r1

Revhuydprv txh rv ydoruhv gr sduåphwur pìglr � qær pxgdudp vxevwdqfldophqwh1

R lpsruwdqwh ì yhul�fdu txh r hihlwr dohdwöulr hvwä ehp fdudfwhul}dgr qr prghor

Page 83: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

:; FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

P4 frp d srvwhulrul gh �! ud}rdyhophqwh glvwdqwh gd iurqwhlud �! @ 31 R phv0

pr rfruuh frp r sduåphwur �� qr prghor P51 Txdqgr r prghor P6 frqvlghud

dperv rv hihlwrv/ dsduhqwhphqwh rv hihlwrv dohdwöulrv sxurv vær pdlv lpsruwdqwhv

qd frpsrvlêær grv ulvfrv uhodwlyrv txh rv hihlwrv hvsdfldlv gh odujd hvfdod1 Ydprv

prvwudu txh lvwr qær ì yhugdgh d vhjxlu1

Ghyh vhu qrwdgr hqwuhwdqwr txh xpd frpsdudêær gluhwd hqwuh dv srvwhulrulv gh

�! h gh �� qær ì lqwhludphqwh fruuhwr srlv �� uhihuh0vh d xp ydulåqfld frqglflrqdo

gh �l hqtxdqwr txh �! hvwä dvvrfldgr frp xpd ydulåqfld pdujlqdo1 R pdlv fruuhwr/

h iäflo gh vhu ihlwr hp ZlqEXJV ì prqlwrudu dojxpd txdqwlgdgh txh srvvd phglu

d lpsruwåqfld uhodwlyd gr hihlwr hvsdfldo hp frqwudvwh frp r hihlwr qær hvsdfldo1

Sru h{hpsor/ d glvwulexlêær d srvwhulrul gdv txdqwlgdghv

$ @��

�� . �!rx hqwær $3 @

�5�

�5� . �

5!

srgh vhu rewlgr frp dv vhjxlqwhv olqkdv dglflrqdlv gh fögljr qr surjudpd prvwudgr

dqwhulruphqwh=

vg1hps1hvs ?0 vg+e^`,

ydu1hps1hvs ?0 srz+vg1hps1hvs/5,

vg1hps1qdrhvs ?0 vg+j^`,

ud}dr1gs ?0 vg1hps1hvs2+vg1hps1hvs.vg1hps1qdrhvs,

ud}dr1ydu ?0 ydu1hps1hvs2+ydu1hps1hvs.ydu1hps1qdrhvs,

ydu1hps1qdrhvs ?0 srz+vg1hps1qdrhvs/5,

Rv sduåphwurv $ h $3 hvwær hqwuh 3 h 4 h xp ydoru ljxdo d 3=8 lqglfd frqwulexlêøhv

lgíqwlfdv grv grlv hihlwrv dohdwöulrv/ hvsdfldo h qær hvsdfldo/ sdud d yduldêær gr ulvfr1

D Iljxud 719 prvwud d hvwlpdwlyd gd ghqvlgdgh d srvwhulrul d sduwlu gd dprvwud

PFPF grv grlv sduåphwurv dflpd/ $ + juä�fr vxshulru, h $3 +juä�fr lqihulru,1 Dv

gxdv glvwulexlfrhv hvwær orfdol}dgdv qd sduwh vxshulru gr lqwhuydor +3>4,/ lqglfdqgr

xpd qðwlgd suhsrqghuåqfld gd frqwulexlêær hvsdfldo sdud dv glihuhqfdv gh ulvfr

qr pdsd gh Vær Sdxor1 Dvvlp/ d pdlru sduwh gd yduldêær ghyh vhu dwulexðgd d

fdxvdv txh h{wudsrodp rv olplwhv grv pxqlfðslrv frqvwlwxlqgr0vh hp idwruhv gh

odujd hvfdod1

Page 84: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7181 H[HPSOR :<

omega

dens

idad

e a

post

erio

ri

0.70 0.75 0.80 0.85 0.90 0.95 1.00

05

1015

20

omega linha

dens

idad

e a

post

erio

ri

0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00

05

1015

2025

30

Iljxud 719= Hvwlpdwlyd gh ghqvlgdgh gd frqwulexlêær uhodwlyd gr hihlwr dohdwöulr

hvsdfldo phglgr dwudyìv gd phglgd rphjd gh�qlgd qr wh{wr1 Juä�fr vxshulru

fruuhvsrqgh dr ghvylr sdguær h juä�fr lqihulru/ d ydulåqfld=

Page 85: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

;3 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

719 H{whqvøhv= prghorv gh hvsdêr h whpsr

Xpd gdv judqghv ydqwdjhqv gd irupxodêær ed|hvldqd ì vxd idflolgdgh sdud vhu

jhqhudol}dgr sdud prghorv pdlv frpsolfdgrv1 Xpd ghvwdv h{whqvøhv ì txdqgr rv

gdgrv yduldp wdqwr qr hvsdêr txdqwr qr whpsr1 Ydprv hqfhuudu hvwh fdsðwxor

frp xp prghor xvdgr hp Dvvxqêær h Uhlv +5334, rqgh xp prghor gh hvsdêr h

whpsr surgx}lx uhvxowdgrv qrwäyhlv qd dqäolvh hvwdwðvwlfd1 Hvwh prghor ì edvhdgr

hp sursrvwd dqwhulru gh Ehuqdglqhool hw do1 +4<<8,1

Ohlvkpdqlrvh Ylvfhudo ì xpd grhqêd }rrqöwlfd wðslfd gh äuhdv uxudlv1 Qr

Eudvlo/ yäulrv fhqwurv xuedqrv/ lqfoxlqgr Ehor Krul}rqwh/ frphêdudp d uhjlvwudu

fdvrv ghvwd grhqêd1 Xwlol}dqgr rv surfhglphqwrv uhfrphqgdgrv shod Rujdql}dfçr

Pxqgldo gh Vdýgh/ d Suhihlwxud gh Ehor Krul}rqwh frphêrx d whu fxvwrv fuhvfhqwhv

d phglgd txh d hslghpld vh ghvhqyroyld frp 493 fdvrv +h 4: pruwhv, uhjlvwudgrv

hqwuh 4<<7 h 4<<:1 Hp 4<<8/ r surjudpd gh suhyhqfçr fxvwrx 4/8 plokær gh

göoduhv1 Frqvlghudqgr r dowr fxvwr hqyroylgr/ irl qhfhvväulr sulrul}du äuhdv h id}hu

suhglêøhv gr ghvhqyroylphqwr gd grhqêd qrv suö{lprv dqrv1 Frpr r qýphur gh

fdvrv ì shtxhqr hp fdgd äuhd/ dv wd{dv vær pxlwr lqvwäyhlv1

Ehor Krul}rqwh irl sduwlflrqdgd hp 44: äuhdv gh deudqjíqfld/ äuhdv uhodwlyd0

phqwh krprjíqhdv frp lqirupdêær srsxodflrqdo iruqhflgd shor Fhqvr1 Rv fdvrv

kxpdqrv gh Ohlvkpdqlrvh Ylvfhudo irudp jhrfrgl�fdgrv gh dfrugr frp vxd äuhd

gh uhvlgíqfld h gdwd gh sulphlurv vlqwrpdv gd grhqêd1 Rv shuðrgrv gh whpsr vær 45

phvhv d sduwlu gr phlr gr dqr grv shuðrgrv 4<<724<<8/ 4<<824<<9 dqg 4<<924<<:1

Dvvxpd txh rv fdvrv [l vhjxhp xpd glvwulexlêær gh Srlvvrq=

+[lmSl> �l, � Srlvvrq +Sl �l,

rqgh Sl ì d srsxodêær gd äuhd h �l ì d wd{d vxemdfhqwh qd äuhd l/ l @ 4> = = = > Q 1 Dgl0

flrqdphqwh/ dvvxpd txh hodv vær lqghshqghqwhv/ frqglflrqdophqwh qrv sduåphwurv1

Ghqrwh sru [ d pdwul} frp hohphqwr [lw uhsuhvhqwdqgr r qýphur gh fdvrv qd

äuhd l qr whpsr w> l @ 4> ===>44: h w @ 4/ 5/ 61 Vlploduphqwh/ gh�qd d pdwul} S frp

hohphqwr Slw uhsuhvhqwdqgr d srsxodêær gd äuhd l qr whpsr w1 Ilqdophqwh/ gh�qd

Page 86: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7191 H[WHQVØHV= PRGHORV GH HVSDÊR H WHPSR ;4

d pdwul} H frp hohphqwr �lw uhsuhvhqwdqgr d wd{d vxemdfhqwh1

Qöv dgrwdprv xp prghor gh srolq÷plr gh vhjxqgr judx sdud d hyroxêær gdv

wd{dv frp frh�flhqwhv hvshfð�frv sdud fdgd äuhd1 Dvvlp/

�lw @ oq +�lw, @ �l . �l+w � 4, . �l+w� 4,5> +7146,

sdud l @ 4> ===>44: h w @ 4> 5>61 Qöv ghqrwdprv sru �>�> h � rv yhwruhv frp wrgrv

rv �l/ �l h �l/ uhvshfwlydphqwh1

Frpr rv frh�flhqwhv gr srolq÷plr vær hvshfð�frv sru äuhd/ lvwr shuplwh txh

fdgd äuhd srvvxd vhx suösulr shu�o hyroxwlyr/ vhmd gh dxphqwr/ ghfuìvflpr rx

hvwdelolgdgh qr whpsr1 Lvwr wdpeìp lpsolfd txh qöv hvwdprv shuplwlqgr lqwhudêær

hqwuh hvsdêr h whpsr srlv r hihlwr gr whpsr qær vhuä r phvpr hp äuhdv glihuhqwhv1

Revhuyh wdpeìp txh h{lvwhp pdlv sduåphwurv txh gdgrv qhvwh sureohpd1 Sdud

wruqdu r prghor lghqwl�fäyho/ qöv lpsrprv uhvwulêøhv dwudyìv gdv glvwulexlêøhv d

sulrul1

Qöv dvvxplprv txh rv frh�flhqwhv gr srolq÷plr srvvxhp glvwulexlfær pdunr0

yldqd=

i+�4> ===> �44:m��, 2 h{s

3C���5

[l�m

+�l ��m,5

4D >

i+�4> ===> �44:m��, 2 h{s

3C���5

[l�m

��l � �m

�54D > +7147,

i+�4> ===> �44:m��, 2 h{s

3C���5

[l�m

��l � �m

�54D =

h r uhvwr fdl hp fdvfdwd frpr qrv prghorv dqwhulruhv1

Uhvxplqgr rv uhvxowdgrv gh Dvvxqêær h Uhlv +5334,/ srghprv gl}hu txh/ hq0

txdqwr rv pdsdv gdv wd{dv euxwdv hudp sudwlfdphqwh lqýwhlv sdud hoderudu sroðwl0

fdv gh sulrul}dêær gh äuhdv gdgd vxd dowd yduldeloldgh/ rv pdsdv vxdyl}dgrv shod

wëfqlfd ed|hvldqd dsuhvhqwdudp uhvxowdgrv vxusuhhqghqwhphqwh erqv1 Doìp glvwr/

dr id}hu d suhglêær gr qýphur gh fdvrv sdud r dqr gh 4<<;/ r dfhuwr irl pxlwr

erp1 Glvfxvvær vreuh irupdv gh vhohêær gh prghorv srgh vhu olgd qr duwljr dflpd1

Page 87: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

;5 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

Dsuhvhqwdqgr dshqdv xp grv uhvxowdgrv gr dmxvwh ed|hvldqr ghvwh prghor/

frqvlghuh d Iljxud 71: txh prvwud d hyroxêær gdv wd{dv gh fdgd äuhd frqhfwdgdv

frpr xpd olqkd1 R juä�fr gr fhqwur ì r gdv wd{dv euxwdv/ xp hpdudqkdgr gh

olqkdv txh ghl{d fodur d lphqvd yduldêær ghvwdv wd{dv1 R juä�fr lqihulru/ xvdqgr

rv phvprv gdgrv pdv r prghor ed|hvldqr frp xp srolq÷plr gh sulphlur judx

sdud dqäolvh/ frqvhjxh h{wudlu pxlwr pdlv lqirupdêær ýwlo srvvlelolwdqgr rulhqwdu

d dêær sýeolfd qd äuhd gh vdýgh1 R juä�fr vxshulru ì r prghor ed|hvldqr frp

xp srolq÷plr gh vhjxqgr judx1 R srolq÷plr dfderx vhqgr suhihulgr shor qrvvr

fulwìulr gh hvfrokd gh prghorv1

Qöv yhprv dojxpdv glihuhqfdv lpsruwdqwhv hqwuh qrvvr prghor h rxwurv txh yhp

vhqgr xvdgrv qd olwhudwxud +Zdoohu hw do/ 4<<:> [ld h Fduolq/ 4<<;> Nqruu0Khog h

Ehvdj/ 4<<;,1 Sdud loxvwudu dv glihuhqêdv/ ydprv holplqdu dojxdpv frpsolfdêøhv

hqyroylgdv frp d suhvhqfd gh fryduläyhlv h hvwudwrv gh sdgurql}dêær qhvwhv duwl0

jrv1 Dvvlp/ hp qrvvd qrwdêær/ r prghor gh [ld h Fduolq +4<<;, �fd uhgx}lgr d

�lw @ � . �w . !wl rqgh/ gdgrv rv klshusduåphwurv/ r frqmxqwr i!w4> = = = > !

wqj srv0

vxl xpd glvwulexlêær hvsdfldo FDU qr whpsr w h rv frqmxqwrv vær lqghshqghqwhv

hp prphqwrv glihuhqwhv gr whpsr1 Sruwdqwr/ d lqwhudêær hvsdêr0whpsr dsduhfh

frpr hvwuxwxud hvsdfldo pxgdqgr qr whpsr1 Dr lqyìv gh prghodu d pxgdqfd

whpsrudo/ hohv ghl{dp !w4 h !w.4

4 wrwdophqwh glvvrfldgrv qd sulrul h qd yhurvvlplo0

kdqêd1 R phvpr wdpeìp rfruuh frp r prghor gh Zdoohu hw do1+4<<:, txh wruqd0vh

�lw @ �wl . !

wl rqgh �

wl vær hvsdfldophqwh qær hvwuxwxudgrv h !

wl vhjxh xpd glv0

wulexlêær FDU hp fdgd prphqwr gh whpsr h dperv rv frqmxqwrv/ i�w4> = = = > �wqj h

i!w4> = = = > !wqj vær lqghshqghqwhv qr whpsr gdgrv rv klshusduåphwurv1 Mä r prghor

sursrvwr sru Nqruu0Khog dqg Ehvdj +4<<;, uhgx}0vh d �lw @ �w . �l . !l rqgh �l

vær hvsdfldophqwh qær hvwuxwxudgrv h !l vhjxh xpd glvwulexlêær FDU1 Hvwd ýowl0

pd derugdjhp qær prghod d lqwhudfær hvsdêr0whpsr srlv rv hihlwrv gh hvsdêr h

whpsr vær dglwlyrv1 Hp frqwudvwh/ Dvvxqêær h Uhlv +5334, shuplwhp d lqwhudêær

hvsdêr0whpsr qd irupd gh shu�v hyroxwlyrv hvshfð�frv gh fdgd äuhd txh yduldp

vxdyhphqwh qr hvsdêr1

Page 88: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7191 H[WHQVØHV= PRGHORV GH HVSDÊR H WHPSR ;6

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

o

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

o

t (tim

e)

estimated rate (linear model)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

area

36ar

ea43

area

44ar

ea55

area

64ar

ea74

area

97

0.0

0.5

1.0

1.5

2.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

0.00.00050.00100.0015o

oo

oo

o

o

oo

oo

oo

o

oo

oo

oo

oo

o

oo

oo

o

o

o

oo

oo

o

o

o

o

o

o

oo

oo

o

o

o

o

o

o

oo

o

o

o

oo

o

o

oo

o

o

o

o

oo

oo

oo

o

oo

o

o

o

o

oo

o

o

oo

oo

o

o

o

oo

o

oo

o

o

t (tim

e)

cases/pop

0.0

0.5

1.0

1.5

2.0

0.00.00050.00100.0015

area

36ar

ea43

area

44ar

ea55

area

64ar

ea74

area

97ar

ea14

0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

o

o

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

o

o

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

t (tim

e)

estimated rate (quadratic model)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00.00050.00100.0015

area

36ar

ea43

area

44ar

ea55

area

64ar

ea74

area

97ar

ea14

0

Iljxud 71:= Juä�fr gd hyroxêær gdv wd{dv gh lqflgíqfld gh Ohlvkpdqlrvh Ylvfhudo

hp Ehor Krul}rqwh gh 4<<8 d 4<<; gh dfrugr frp wuív prghorv= Ed|vldqr olqhdu

+hvtxhugd,/ wd{dv euxwdv +fhqwur, h ed|hvldqr sdudeöolfr +gluhlwd,

Page 89: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

;7 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

Wdehod 715= Wdehod frp rv txdwur pdsdv/ phvpd hvfdod/ gh pruwdolgdgh lqidqwlo

sru pxqlfðslrv hp Vær Sdxor hp 4<<:1 +4, Wd{d euxwd/ +5, P4/ +6, P5/ +7, P6

Page 90: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

7191 H[WHQVØHV= PRGHORV GH HVSDÊR H WHPSR ;8

Wdehod 716= Wdehod frp rv txdwur pdsdv/ hvfdodv glihuhqwhv/ gh pruwdolgdgh lqidqwlo

sru pxqlfðslrv hp Vær Sdxor hp 4<<:1 +4, Wd{d euxwd/ +5, P4/ +6, P5/ +7, P6

Page 91: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

;9 FDSÐWXOR 71 PDSDV ED\HVLDQRV GH GRHQÊDV

prghor qö pìgld GS 518( phgldqd <:18(

� 061;6 3135 061;: 061;6 061:<

P4 �! 4818: 5175 44173 48177 53199

�! 3159 3135 3155 3158 315<

� 061;; 3135 061<4 061;; 061;7

P5 � � 8174 3138 7144 8163 :158

�� 3176 3136 316: 3176 317<

� 061;; 3135 061<4 061;; 061;8

�! 9177 414< 7185 915< <14<

P6 � � 4:719 4351; 7:19: 4841; 73<13

�! 3173 3137 3166 3173 317:

�� 313< 3136 3138 313; 3147

Wdehod 717= Wdehod frp rv uhvxowdgrv grv dmxvwhv grv prghorv P4/ P5 h P6

Page 92: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

Fdsðwxor 8

������ �� ������������

Sur�vvlrqdlv gh vdýgh sýeolfd iuhtxhqwhphqwh vær fkdpdgrv d lqwhuylu hp uhjløhv

txh sduhfhp srvvxlu xpd wd{d gh rfruuíqfld gh djudyrv ã vdýgh dflpd gr txh ì

hvshudgr qxp gdgr shuðrgr gh whpsr1 Jhudophqwh/ qr fäofxor gr qýphur hvshu0

dgr gh rfruuíqfldv/ ohyd0vh hp frqvlghudêær rv idwruhv gh ulvfr txh vdelgdphqwh

dihwdp d lqflgíqfld grv hyhqwrv/ wdlv frpr= d glvwulexlêær sru lgdgh h vh{r gd srs0

xodêær uhvlghqwh/ r whpsr gh h{srvlêær d dojxp djhqwh hwlroöjlfr frqkhflgr/ hwf1

Surfxudqgr rulhqwdu d dêær gd vdýgh sýeolfd qhvwdv vlwxdêøhv/ rv hvwxgrv gh gh0

whfêær gh frqjorphudgrv gh grhqêdv jdqkdudp edvwdqwh dwhqêær grv shvtxlvdgruhv

qrv ýowlprv dqrv1 Sru h{hpsor/ r sureohpd gd djuhjdêær hvsdfldo gh ohxfhpldv

h olqirpdv wíp vlgr hvwxgdgr frp iuhtÿíqfld1 Gh lqwhuhvvh hvshfldo whp vlgr d

whqwdwlyd gh yhul�fdu d klsöwhvh gh txh hvwdv grhqêdv srvvxhp xpd fdxvd yludo

dwudyìv gh whvwhv gh txh d glvwulexlêær hvsdfldo grv fdvrv ì dohdwöuld rx srvvxl

frqjorphudgrv gh dowd lqflgíqfld1 Hvwä lpsoðflwd d vxsrvlêær gh txh d klsöwhvh

gh ruljhp yluöwlfd ohyd lphgldwdphqwh d frqjorphudgrv/ vxsrvlêær hvwd txh whp

vlgr frqwhvwdgd pdlv uhfhqwhphqwh/ whqgr hp ylvwd uhvxowdgrv gh shvtxlvd vreuh

rv phfdqlvprv gh wudqvplvvær yludo h d h{lvwíqfld gh orqjrv shuðrgrv gh odwíqfld

txh dpruwhfhp d irupdêær gh frqjorphudgrv dr orqjr gr whpsr1 Hqwuhwdqwr/ rv

hvwxgrv gh frqjorphudgrv vær lpsruwdqwhv srlv ì gh lqwhuhvvh lghqwl�fdu äuhdv gh

ulvfr pdlv hohydgr hp phlr d uhjløhv pdlruhv gh ulvfr dsur{lpdgdphqwh frqvwdqwh

;:

Page 93: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

;; FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

sdud uhdol}du hvwxgrv pdlv sruphqrul}dgrv qdv äuhdv lghqwl�fdgdv1 Xp phokru

hqwhqglphqwr gd hvwuxwxud gh frqjorphudgrv hvsdfldlv gh xpd grhqêd ohyd d xpd

dqäolvh pdlv remhwlyd gh txdotxhu vxvshlwd gh h{fhvvr gh ulvfr1

Hp sduwlfxodu/ d revhuydêær gh xp qýphur ehp pdlru gr txh r hvshudgr

gh fdvrv gh ohxfhpld lqidqwlo dr uhgru gh xpd lqvwdodêær qxfohdu hp Vhood�hog

+Lqjodwhuud, ohyrx d xpd judqgh frqwuryìuvld h vhuylx frpr srghurvr dujxphqwr

sdud d fuldêær gh xp vlvwhpd lqjoív sdud frohwdu gdgrv gh lqflgíqfld h pruwdo0

lgdgh hp shtxhqdv äuhdv jhrjuä�fdv1 Hvwh fdvr jhurx judqgh lqvdwlvidêær hqwuh

hslghplöorjrv h hvwdwðvwlfrv srlv r frqjorphudgr qær irl ghwhfwdgr shor vlvwhpd

gh yljloåqfld hslghplroöjlfd h{lvwhqwh h fkhjrx dr sýeolfr dwudyìv gh xp surjud0

pd gh whohylvær1 D sulqflsdo prwlydêær hud d rfruuíqfld gh 7 fdvrv gh ohxfhpld

lqidqwlo uhjlvwudgrv qr shtxhqr zdug gh Vhdvfdoh hqwuh 4<9; h 4<;5/ txdqgr hudp

hvshudgrv dshqdv 315 fdvrv qhvwh shuðrgr1 Hvwh hslvöglr irl dpsodphqwh glvfxwlgr

qxp qýphur gr Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw| +Jdugqhu/ 4<;<, h pxlwrv

ghvhqyroylphqwrv hvwdwðvwlfrv dsduhfhudp qr frqwh{wr ghvwh fdvr hvshfð�fr1

Dv äuhdv gh ulvfr vljql�fdwlydphqwh hohydgr pdv qær hvshudgr +rx qær h{solfd0

gr, uhfhehp r qrph gh frqjorphudgrv1 Hohv srghp vhu sxudphqwh whpsrudlv +vh

r hvsdêr ì ljqrudgr, rx srghp vhu dqdolvdgrv ohydqgr0vh hp frqwd wdqwr r hvsdêr

txdqwr r whpsr1 Nqr{ +4<;;, gh�qh xp frqjorphudgr +foxvwhu/ hp lqjoív, frpr

xp juxsr gh rfruuíqfldv jhrjud�fdphqwh olplwdgr gh wdpdqkr h frqfhqwudêær wdlv

txh vhmd lpsuryäyho gh rfruuhu sru phur dfdvr1 Lqihol}phqwh/ hvwd gh�qlêær qær

srvvxl xp fduäwhu rshudflrqdol}äyho hperud hod vxjlud pìwrgrv edvhdgrv hp whvwhv

gh klsöwhvhv sdud lghqwl�fdu rv frqjorphudgrv1 Gh idwr/ d pdlruld grv pìwrgrv

h{lvwhqwhv vær edvhdgrv hp whvwhv gh vljql�fåqfld rx whvwhv gh klsöwhvhv1 D olwhu0

dwxud qr dvvxqwr ì ydvwd h ydprv dsuhvhqwdu dshqdv dojxqv grv sulqflsdlv pìwrgrv

sursrvwrv dwì r prphqwr1

Rv pìwrgrv gh ghwhfêær gh frqjorphudgrv glylghp0vh hp gxdv fdwhjruldv

jhudlv1 R sulphlur juxsr gh pìwrgrv ì dtxhoh hp txh rv gdgrv vær frohwdgrv

sdud whvwdu d klsöwhvh gh xp srvvðyho h{fhvvr dr uhgru gh xpd irqwh vxvshlwd h

hvwd irqwh ì lghqwl�fdgd dqwhv gh revhuydu rv gdgrv1 Hohv vær fkdpdgrv gh whvwhv

irfdgrv gh frqjorphudgrv1 R vhjxqgr juxsr gh pìwrgrv surfxud lghqwl�fdu dv

Page 94: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

;<

äuhdv jhrjuä�fdv frp xp ulvfr vljql�fdwlydphqwh hohydgr vhp hvshfl�fdu gh dq0

whpær txdlv h txdqwdv äuhdv vhuldp hvwdv1 Hohv vær fkdpdgrv gh whvwhv jhqìulfrv

gh frqjorphudgrv1 Dv glihuhqfdv hqwuh rv grlv juxsrv gh pìwrgrv srgh vhu pho0

kru hqwhqglgdv frqvlghudqgr dv gxdv shujxqwdv txh rv vhxv whvwhv gh klsöwhvhv

dvvrfldgrv surfxudp uhvsrqghu=

� Rv whvwhv irfdgrv surfxudp uhvsrqghu/ frp xp vlp rx xp qær/ d vhjxlqwh

shujxqwd= h{lvwh hylgíqfld qrv gdgrv gh txh dr uhgru gd irqwh vxvshlwd/ or0

fdol}dgd qd srvlêær {3/ kä xp dxphqwr vljql�fdwlyr gr ulvfr gh fhuwd grhqêd

B R ixqgdphqwdo ì txh d srvlêær {3 vhmd frqkhflgd dqwhv gh vh revhuydu rv

gdgrv1

� Rv whvwhv jhqìulfrv surfxudp uhvsrqghu/ frp xp vlp rx xp qær/ d hvwd

rxwud shujxqwd= h{lvwh hylgíqfld qrv gdgrv gh txh xpd rx pdlv uhjløhv gr

pdsd/ qdr lghqwl�fdgdv suhyldphqwh/ srvvxhp xp ulvfr vljql�fdwlydphqwh

pdlru txh r ydoru pìglr revhuydgr qr pdsd frpr xp wrgr B

Sdud dperv rv wlsrv gh whvwhv r prghor qxor ì r phvpr/ r gh dxvíqfld gh

frqjorphudgrv frp r sdguær hvsdfldo gd grhqêd vhqgr wrwdophqwh fdvxdo1 Txdo

r vhqwlgr suhflvr ghvwd d�updêær B Ì r gh txh d wd{d gh lqflgíqfld sru shvvrd ì

frqvwdqwh hp wrgrv rv orfdlv/ lpsolfdqgr txh r qýphur hvshudgr gh fdvrv hp xp

orfdo ì sursruflrqdo dr qýphur gh shvvrdv hp ulvfr prudqgr qhvwh orfdo1 Vxsrqkd

txh d uhjlær gh hvwxgr ì glylglgd hp q äuhdv h ghqrwh r qýphur revhuydgr gh fdvrv

hp fdgd xpd ghodv sru |l h r qýphur hvshudgr gh fdvrv sru Hl> l @ 4> ===> q1 VhmdQl

r qýphur wrwdo gh shvvrdv0dqr hp ulvfr qd äuhd l h vhmd � d wd{d dqxdo lqglylgxdo

+rx shu fdslwd, gh rfruuíqfld gd grhqêd1 R prghor qxor gh dohdwrulhgdgh frpsohwd

rx dxvíqfld gh frqjorphudgrv ì h{suhvvr frpr vhqgr d klsöwhvh qxod

K3 = |l � Srlvvrq+Hl @ �Ql,> lqghshqghqwhv> l @ 4> ===> q

Rv whvwhv vær hvshfl�fdgrv whqgr hp phqwh dv dowhuqdwlydv gh lqwhuhvvh1 Qr

fdvr grv whvwhv irfdgrv/ hvshud0vh txh d wd{d lqglylgxdo � qdr vhmd frqvwdqwh pdv

txh ydulh frp l/ dxphqwdqgr txdqwr pdlv suö{lpr iru d äuhd l gd irqwh vxvshlwd1

Page 95: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

<3 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

Rv whvwhv jhqìulfrv dvvxphp dshqdv txh h{lvwhp xpd rx pdlv uhjløhv rqgh r ydoru

gh � ì pdlv hohydgr txh qr uhvwdqwh gr pdsd1 Revhuyh txh/ qhvwh vhjxqgr fdvr/

qær hvwä h{foxðgd d klsöwhvh dowhuqdwlyd gh khwhurjhqhlgdgh hvsdfldo/ d vlpsohv

yduldelolgdgh gdv wd{dv hqwuh dv äuhdv1 Hqwuhwdqwr/ hvwduhprv pdlv lqwhuhvvdgrv/

h lvwr hvwduä uh hwlgr qdv hvwdwðvwlfdv gh whvwh/ qdv dowhuqdwlydv pdlv uhdolvwdv gh

dxwrfruuhodêær hvsdfldo hp txh dv wd{dv gh äuhdv yl}lqkdv vær vlploduhv1

H{dpsoh 43 Irl uhjlvwudgr sru yrowd gh 4<;7 xp hohydgr qýphur gh fdvrv gh

ohxfhpld gh 3 d 4< dqrv dr uhgru gh 45 ghsövlwrv gh ol{r wö{lfr frqwdplqdgrv

frp xp frpsrvwr rujåqlfr yroäwlo fkdpdgr wulforurhwk|ohqr1 R Ghsduwdphqwr gh

Vdýgh gr Hvwdgr gh Qryd \run lqlflrx xpd vìulh gh hvwxgrv sdud dyhuljxdu r fdvr

h fuldu xpd sroðwlfd suö0dwlyd gh vdýgh/ hp frqwudvwh frp xpd sroðwlfd uhdwlyd1

Hvwxgrx0vh r shuðrgr gh 4<:; 0 4<;5 qxpd uhjlær frp srxfr pdlv gh 4 plokær gh

shvvrdv hqwuh 3 h 4< dqrv1D uhjlær ì glylglgd hp :<3 äuhdv h uhjlvwurx 8<5 fdvrv

gh ohxfhpld qr shuðrgr1 Dshqdv d äuhd gh uhvlgíqfld gr fdvr hud frqkhflgd1

Ydprv xwlol}du hvwh h{hpsor dr orqjr ghvwh fdsðwxor sdud loxvwudu dojxqv grv

pìwrgrv dsuhvhqwdgrv1 D txhvwær gh lqwhuhvvh ì vdehu vh h{lvwhp frqjorphudgrv

gh ulvfr pdlv hohydgr qd äuhd +whvwh jhqìulfr, h/ hp sduwlfxodu/ vdehu vh h{lvwh

hylgíqfld gh ulvfr pdlv hohydgr hp yrowd grv 45 ghsövlwrv gh ol{r wö{lfr +whvwh

irfdgr,1

Sduwh grv gdgrv sdud d dqäolvh hvwdwðvwlfd frqvlvwh gh xpd wdehod frp :<3

olqkdv/ xpd sru äuhd/ h flqfr froxqdv= lghqwl�fdgru gh äuhd/ frrughqdgdv { h |/

wdpdqkr gd srsxodêær uhvlghqwh qd äuhd h qýphur gh fdvrv gh ohxfhpld revhuydgrv

qd äuhd1 D Wdehod 814 prvwud dv flqfr sulphludv olqkdv gd wdehod gh gdgrv1 D rxwud

sduwh grv gdgrv fruuhvsrqgh dv srvlêøhv jhrjuä�fdv grv 45 ghsövlwrv gh ol{r1

H{dpsoh 44 Prqwhlur0gh0Fdvwur hw do1 +5334, dqdolvdudp rv uhjlvwurv gh uhvlgíq0

fldv gh grdgruhv gh vdqjxh gd Ixqgdêær Khprplqdv gh Ehor Krul}rqwh txh hv0

wdydp lqihfwdgrv frp r yðuxv KWOY L2LL1 Fdgd grdgru lqihfwdgr/ ghqrplqdgr

fdvr/ whyh vxd uhvlgíqfld pdufdgd frpr xp hyhqwr qr pdsd gh Ehor Krul}rqwh1

Dr phvpr whpsr/ xpd dprvwud gh grdgruhv txh qær hudp lqihfwdgrv shor yðuxv/

ghqrplqdgrv lqglyðgxrv gh frqwuroh/ wdpeìp wlyhudp vxdv uhvlgíqfldv pdufdgdv

Page 96: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

<4

Iljxud 814= Pdsd gh uhjlær dr uhgru gh Qryd Lrutxh frp srvlêøhv grv fhqwuölghv

gdv äuhdv lqglfdgdv sru xp srqwr h rv orfdlv gh surfhvvdphqwr gh ol{r frqwhqgr

wulfkorurhwk|ohqh lqglfdgr sru { +Zdoohu hw do1/ 4<<5,

Äuhd { | srsxodêær fdvrv

4 713: 09:168 6873 6

5 7197 0991;9 6893 7

6 81:4 0991<; 6:6< 4

7 :194 099133 5:;7 4

8 :165 09:165 58:4 6

Wdehod 814= Wdehod frp dv flqfr sulphludv olqkdv gh gdgrv uhihuhqwhv dr h{hpsor

gh ohxfhpld qr qruwh gr hvwdgr gh Qryd \run +Zdoohu hw do1/ 4<<5,1

Page 97: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

<5 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

Iljxud 815= Pdsd gh uhjlær dr uhgru gh Qryd Lrutxh frp srvlêøhv grv fhqwuölghv

gdv äuhdv hp txh kdyld shor phqrv xp fdvr lqglfdgdv sru xp srqwr1 Äuhdv rqgh

fdvrv qær irudp uhjlvwudgrv qær vær prvwudgdv1 +Zdoohu hw do1 4<<5,

Page 98: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

<6

frpr hyhqwrv1 Xpd shujxqwd gh lqwhuhvvh qhvwh sureohpd ì vdehu vh r sdguær hv0

sdfldo gh uhvlgíqfldv grv lqihfwdgrv ì glihuhqwh gr sdguær hvsdfldo gh uhvlgíqfldv

grv lqglyðgxrv vhuylqgr frpr frqwurohv1 Xpd glihuhqêd qr sdguær hvsdfldo hqwuh

rv grlv juxsrv/ fdvrv h frqwurohv/ srgh h{lvwlu vh/ sru h{hpsor/ dojxp h{lvwlu dojxp

idwru hwlroöjlfr txh ì glvwulexðgr qd srsxodêær gh irupd hvsdfldophqwh glihuhqfld0

gd1 Vh irvvh revhuydgr txh r judx gh frqfhqwudêær gh fdvrv qd shulihuld ì pdlru

txh dtxhoh revhuydgr qd dprvwud gh frqwurohv/ xpd srvvðyho h{solfdêær sdud lvwr

srghuld hvwdu dvvrfldgd ã glqåplfd pljudwöuld gd flgdgh1 Vxsrqkd txh d sured0

elolgdgh gh xp lqglyðgxr vhu lqihfwdgr whp uhodêær frp vhx sdvvdgr pljudwöulr/

pljudqwhv gr Qruwh gh Plqdv Jhudlv whqgr xpd fkdqfh pdlv dowd gh vhuhp lqihf0

wdgrv1 Rv pljudqwhv qær hvwær glvwulexðgrv gh irupd wrwdophqwh fdvxdo qd flgdgh

srlv h{lvwhp uhodwlydphqwh pdlv pljudqwhv qd shulihuld gd flgdgh gh Ehor Krul0

}rqwh1 Dvvlp/ r sdguær hvsdfldo gd lqihfêær srghuld vhu h{solfdgr sru xp idwru

hwlroöjlfr/ d pljudêær/ txh hvwä glvwulexðgd gh irupd hvsdfldophqwh glihuhqfldgd1

Hqfrqwudu frqjorphudgrv gh lqihfwdgrv hud sruwdqwr gh lqwhuhvvh hslghplöorjlfr

sdud wudêdu r shu�o ghvwh yðuxv qr Eudvlo1

Xp h{hpsor gh whvwh irfdgr wdpeìp wdpeìp irl frqvlghudgr qhvwh wudedokr1

Xp lqglyðgxr whvwdgr ì frqvlghudgr srvlwlyr sdud r yðuxv KWOY vh hoh ì srvlwl0

yr qxp sulphlur whvwh +Holvd, h ì srvlwlyr wdpeìp qxp vhjxqgr whvwh +Zhvwhuq

Eorw, txh hoh id} qxp vhjxqgr prphqwr1 Qhp wrgrv rv lqglyðgxrv srvlwlyrv qr

sulphlur whvwh +Holvd, uhwruqdudp dr Khprplqdv sdud uhdol}du r vhjxqgr whvwh1

Frpr r khprfhqwur hud orfdol}dgr qr fhqwur gd flgdgh gh Ehor Krul}rqwh/ vxujlx

d klsöwhvh gh txh dv shvvrdv txh prudydp qd shulihuld/ sreuhv hp vxd pdlruld/

whuldp xp pdlru fxvwr gh uhwruqdu dr khprfhqwur sdud xpd vhjxqgd ylvlwd +fxvwr

gh wudqvsruwh/ shugd gh xp gld gh wudedokr/ hwf1,1 Lvwr srghuld vhu whvwdgr dwudyìv

gh xp whvwh txh vxsøh txh d sur{lplgdgh dr khprfhqwur vhuld xp idwru dxphq0

wdyd d fkdqfh gh xp lqglyðgxr ylu d uhwruqdu sdud xp vhjxqgr h{dph1 Lvwr ì/ qd

olqjxdjhp dsuhvhqwdgd qhvwh fdsðwxor/ r khprfhqwur vhuld xp irfr1

D dqäolvh hp Prqwhlur0gh0Fdvwur hw do1 +5334, id} xvr gh whvwhv h pìwrgrv

glihuhqwhv gdtxhohv dsuhvhqwdgrv dtxl srlv rv gdgrv vær gr wlsr fdvr h frqwuroh h

Page 99: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

<7 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

vre d irupd gh surfhvvrv srqwxdlv1 Qær ydprv wudwdu hp ghwdokhv hvwd vlwxdêær

qhvwh fdsðwxor h r duwljr hp txhvwær ghyh vhu frqvxowdgr sdud pdlruhv lqirupdêøhv

shor ohlwru lqwhuhvvdgr1

Dvvlp/ rv whvwhv gh ghwhfêær gh frqjorphudgrv surfxudp uhvsrqghu vh h{lvwh

hylgíqfld gh djorphudêær gh fdvrv dflpd gd djorphudêær txh dsduhfh qdwxudophqwh

ghylgr d glvwulexlêær jhrjuä�fd qær0krprjíqhd gdv srsxodêøhv1Xvxdophqwh/ r fäo0

fxor grv ydoruhv hvshudgrv hp fdgd äuhd ì ihlwr sdgurql}dqgr0vh shod glvwulexlêær

gh lgdgh h vh{r gd vxd srsxodêær/ frpr mä h{solfdprv dqwhv1 D pdlru sduwh grv

hvwxgrv gh frqjorphudgrv txh whp vlgr sxeolfdgd hqyroyh xpd irupd rx rxwud gh

fåqfhu txh dwlqjhp xpd srsxodêær gh irupd glihuhqfldgd sru lgdgh h vh{r1 Dvvlp/

vh d glvwulexlêær hwäuld h sru vh{r hvwä glvsrqðyho h wd{dv uhjlrqdlv rx qdflrqdlv

hvwær glvsrqðyhlv/ d sdgurql}dêær ì xp fxlgdgr eävlfr txh ghyh vhu wrpdgr1

814 Whvwhv jhqìulfrv

H{lvwhp q äuhdv/ |l ì r qýphur revhuydgr gh fdvrv h Hl ì r qýphur hvshudgr gh

fdvrv/ l @ 4> ===> q1 Vhmd Ql r qýphur wrwdo gh shvvrdv0dqr hp ulvfr qd äuhd l1

Vh qær h{lvwh sdgurql}dêær sru lgdgh h vh{r/ Hl 2 Ql1 Vhmd e� @S

|l@S

Ql d

hvwlpdwlyd gd wd{d dqxdo lqglylgxdo +rx shu fdslwd, gh rfruuíqfld gd grhqêd1 Hp

wrgrv rv pìwrgrv/ wrpd0vh � @ e� ljqrudqgr0vh r huur gh hvwlpdêær hqyroylgr mä

txh d ydulåqfld gh e� ì edvwdqwh shtxhqd uhodwlydphqwh d yduldelolgdgh gh |l1 D

orfdol}dêær gd äuhd l ì lghqwl�fdgd frp r vhx fhqwuölgh ghqrwdgr sru {l1

81414 Pìwrgr JDP gh Rshqvkdz

Rshqvkdz hw do1 +4<;;, surs÷v xp pìwrgr lqwhqvlyr frpsxwdflrqdophqwh h frp

judqgh dshor ylvxdo fkdpdgr Jhrjudsklfdo Dqdo|vlv Pdfklqh/ deuhyldgr sru JDP1

Sdud dsolfdu r pìwrgr/ ydprv frqvlghudu Hl 2 Ql/ lvwr ì/ vhp sdgurql}dêær sru

lgdgh h vh{r +d h{whqvær sdud hvwd vlwxdêær ì lphgldwd,1 Lpdjlqh xpd judgh uhjxodu

ehp �qd vreuhsrvwd dr pdsd/ frp qöv uhjxoduphqwh hvsdfdgrv/ h lqgh{dgd sru

m> m @ 4> ===> M 1 Dvvrflh rv ydoruhv gh fdgd äuhd drv vhxv fhqwuölghv1 R surfhglphqwr

vhjxh r dojrulwpr ghvfulwr dedl{r=

Page 100: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8141 WHVWHV JHQÌULFRV <8

� Vhohflrqh xp udlr u +sru h{hpsor/ u @ 4>5> rx 7 np,1

� Hp fdgd qö m gd judgh uhjxodu/ �{h xp fðufxor Fmu gh udlr u1

� Fdofxoh

Rmu @

q[l@4

|lL^{l5Fmu` h Qmu @

q[l@4

QlL^{l5Fmu`

r qýphur gh fdvrv h shvvrdv0dqr gdv äuhdv fxmrv fhqwuölghv fdhp ghqwur gr

fðufxor Fmu/ uhvshfwlydphqwh1

� Fdofxoh r s0ydoru smu dvvrfldgr frp Rmu vre d klsöwhvh qxod=

smu @ S +[ � Rmu, rqgh [ � Srlvvrq +�Qmu,

� Ghvhqkh r fðufxor Fmu vh Rmu � 5 h vh smu � 3=3351

� Uhidêd r surfhglphqwr dflpd dxphqwdqgr hvfrokhqgr rxwur udlr u sdud r

fðufxor1

R uhvxowdgr �qdo ì d lghqwl�fdêær gh äuhdv gh ulvfr sru hpdudqkdgr gh fðufxorv

vreuhsrvwrv/ wrgrv dowdphqwh vljql�fdqwhv h frp shor phqrv grlv hyhqwrv1

H{dpsoh 45 Xvdqgr wuív ydoruhv gh u +4/5/ h 7 np,/ Wxuqexoo hw do1 +4<<3,

h{dplqdudp ;68;: fðufxorv frp rv gdgrv gh Qryd \run1 D Iljxud 34 prvwud rv

836 fðufxorv +319( gr wrwdo, txh irudp vljql�fdwlyrv dr qðyho qrplqdo gh 313351

Hperud fdgd fðufxor vhmd mxojdgr lqglylgxdophqwh vljql�fdwlyr dr qðyho 3=335/

xp qðyho gh vljql�fåqfld sdud wrgrv rv fðufxorv vlpxowdqhdphqwh qær ì frqkhfl0

gr1 D ud}ær ì r frqkhflgr ihq÷phqr gh whvwhv vlpxowåqhrv qær lqghshqghqwhv

txh/ qhvwh fdvr/ ì sduwlfxoduphqwh gliðflo ghylgr dr lphqvr qýphur gh whvwhv hih0

wxdgrv1 Vær uhdol}dgrv U whvwhv hp fdgd qö gh xpd judgh �qd gh wdpdqkr M /

vxsrvwdphqwh edvwdqwh judqgh/ rqgh U ì r qýphur gh udlrv h{shulphqwdgrv +yhmd

h{hpsor,1 Revhuyh txh/ vh xp fðufxor ì ghvhqkdgr/ yäulrv rxwurv fðufxorv yl}lqkrv

vhuær ghvhqkdgrv/ pxlwrv frqwhqgr h{dwdphqwh rv phvprv fdvrv1 D hvfrokd srxfr

frpxp gr srqwr gh fruwh 3=335 sdud r s0ydoru ì duelwuäuld h surfxud frpshqvdu/

gh dojxpd irupd/ hvwh sureohpd gh whvwhv vlpxowåqhrv pdv hvwd hvfrokd fduhfh gh

txdotxhu edvh whöulfd1

Page 101: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

<9 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

Iljxud 816= Uhvxowdgrv gr pìwrgr JDP gh Rshqvkdz hw do1 +4<;;, frp fðufxorv

gh udlrv 4/ 5/ h 7 np txh irudp vljql�fdwlyrv dr qðyho qrplqdo gh 31335 +h{wudðgr

gh Wxuqexoo hw do1/ 4<<3,

Page 102: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8141 WHVWHV JHQÌULFRV <:

Lqihol}phqwh/ d hvfrokd ghvwh srqwr gh fruwh sdud r s0ydoru ì fuxfldo1 Xp

srqwr gh fruwh pxlwr judqgh +wdo frpr r xvxdo 3=38, ohyduld d xp judqgh qýphur

gh idovrv srvlwlyrv +lvwr ì/ d pxlwrv idovrv frqjorphudgrv, hqtxdqwr txh xp s0

ydoru pxlwr shtxhqr ohyduld d pxlwrv idovrv qhjdwlyrv +lvwr ì/ d shughu pxlwrv

frqjorphudgrv uhdlv,1 Qær h{lvwh vroxêær vdwlvidwöuld sdud hvwh sureohpd h r txh

srgh vhu uhfrphqgdgr ì txh r xvxäulr gr pìwrgr h{shulphqwh frp glihuhqwhv

srqwrv gh fruwh sdud yhul�fdu d hvwdelolgdgh grv uhvxowdgrv rewlgrv1 H{lvwh vriwzduh

judwxlwr glvsrqðyho qd lqwhuqhw sdud lpsohphqwdu hvwh surfhglphqwr hp dpelhqwh

XQL[ h Zlqgrzv1

Dv ydqwdjhqv h ghvydqwdjhqv ghvwh pìwrgr srghp vhu uhvxplgdv gd vhjxlqwh

pdqhlud= ì xp pìwrgr vlpsohv gh hqwhqghu/ frp judqgh dshor lqwxlwlyr/ h yl0

vxdophqwh lpsuhvvlrqdqwh> ì xp pìwrgr h{sorudwöulr h qær lqihuhqfldo ghylgr dr

sureohpd gh pxlwrv whvwhv vlpxowåqhrv h ghshqghqwhv lpsolfdqgr hp qðyhlv gh

vljql�fåqfld qrplqdlv> ì lqwhqvlyr frpsxwdflrqdophqwh> rv fðufxorv qær vær lq0

whludphqwh frpsduäyhlv hqwuh vl srlv dv yduläyhlv dohdwöuldv hqyroylgdv srvvxhp

glihuhqwhv glvwulexlêøhv1

D ýowlpd ghvydqwdjhp gd olvwd dflpd srgh vhu plqrudgd vh �{duprv r qxphu0

dgru rx ghqrplqdgru gdv wd{dv gh fdgd fðufxor1 Hvwd ì d sursrvwd gr pìwrgr gh

Ehvdjh h Qhzho/ ghvfulwr d vhjxlu1

81415 Pìwrgr gh Ehvdj h Qhzho

R pìwrgr JDP gh Rshqvkdz �{d r udlr u gr fðufxor h fdofxod r s0ydoru gd

frqwdjhp txh hqfrqwud ghqwur gr fðufxor Fmu 1 Hp whuprv jhudlv/ r pìwrgr gh

Ehvdj h Qhzhoo +4<<4, �{d r qýphur n gh hyhqwrv txh ghyhp vhu exvfdgrv h

fdofxod r udlr qhfhvväulr sdud hqjoreä0orv1 Qr fðufxor uhvxowdqwh/ fdofxod s0ydoru h/

surfhghqgr frpr JDP/ ghvhqkd dshqdv rv fðufxorv vljql�fdwlyrv +s0ydoru � 3=335,1

D vhjxlu/ yduld n sdud yhul�fdu d hvwdelolgdgh grv uhvxowdgrv1

Pdlv hvshfl�fdphqwh/ vxsrqkd txh/ hp wrgd d uhjlær gh hvwxgr/ h{lvwhp F @Sl |l fdvrv h P @

SlQl shvvrdv0dqr hp ulvfr1 Vxsrqkd txh d äuhd l srvvxd

shor phqrv xp fdvr1 Vhmd O d yduläyho dohdwöuld txh frqwd r qýphur gh rxwudv

äuhdv qhfhvväuldv sdud dfxpxodu rv n sulphlurv fdvrv pdlv suö{lprv gh l1 Vhmd o r

Page 103: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

<; FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

ydoru revhuydgr gh O h vhmd p r qýphur gh shvvrdv hp ulvfr qhvvdv o äuhdv1 Vre

r prghor qxor/ r qýphur hvshudgr gh fdvrv qhvvdv o äuhdv ì gdgr sru pF@P 1 R

qýphur Q gh fdvrv qdv sulphludv o äuhdv srvvxl glvwulexlêær gh Srlvvrq frp ydoru

hvshudgr pF@P1 Dvvlp/ S +O � o, @ 4 � S +O A o . 4,1 Pdv lvwr ì vlpsohvphqwh

4 phqrv d suredelolgdgh gh txh dv o sulphludv äuhdv srvvxdp phqrv txh n fdvrv1

Ghvvh prgr/ r s0ydoru ì gdgr sru

4�n�4[m@4

S +Q @ m, @ 4�n�4[m@4

+pF@P,m

m$h�pF@P

Wxuqexoo hw do1 +4<<7, xvdudp hvwh pìwrgr qrv gdgrv gh Qryd \run wrpdqgr

n @ ; h frqvlghudqgr xp frqjorphudgr frpr vljql�fdwlyr vh hoh wlqkdp s0ydoru

phqru txh 31381 Hohv hqfrqwududp 64 frqjorphudgrv vljql�fdwlyrv1 Frpsdudqgr

frp rv uhvxowdgrv gr pìwrgr JDP/ hohv revhuydp txh h{lvwh xpd frqfrugåqfld

jhudo hqwuh rv pdsdv frp pxlwrv grv frqjorphudgrv dqwhulruphqwh vhqgr wdpeìp

ghwhfwdgrv sru hvwh surfhglphqwr dwxdo1

Sru fdxvd gr phvpr sureohpd gh whvwhv vlpxowåqhrv txh dihwd r pìwrgr JDP/

r pìwrgr gh Ehvdj h Qhzho ydl vhpsuh dsuhvhqwdu dojxqv frqjorphudgrv frpr

vljql�fdwlyrv phvpr txh d klsöwhvh qxod vhmd yhugdghlud1 Sdud dolyldu xp srxfr

hvwh sureohpd/ hohv sursxvhudp xp whvwh hvwdwðvwlfr joredo dvvrfldgr frp r qýphur

wrwdo WEQ gh frqjorphudgrv ghwhfwdgrv1 Qr h{hpsor dflpd/ irudp ghwhfwdgrv

64 frqjorphudgrv qrv gdgrv gh Qryd \run1 Hohv fdofxodp xp s0ydoru sdud hvwd

hvwdwðvwlfd vre d klsöwhvh qxod gh dxvíqfld gh frqjorphudgrv1 R ydoru h{dwr gd

hvshudqfd gh WEQ ì iäflo gh vhu fdofxodgd1 Vhmd Lm xpd ixqêær lqglfdgrud gh txh

r fðufxor fhqwudgr qd äuhd m freulqgr rv n fdvrv pdlv suö{lprv ì vljql�fdwlyr1

Hqwær H +WEQ , @Sq

m@4 H +Lm, @Sq

m@4 �m1 Sdud fdofxodu �m/ dsoltxh d iöupxod gr

s0ydoru dflpd sdud rewhu S +O � k, sdud k @ 3>4> === dwì txh r qðyho gh vljql�fåqfld

h{fhgd � sdud k @ k�m 1 R ydoru gh S +O � k

�m , ì r ydoru gh �m1 Qr fdvr grv gdgrv

gh Qryd \run/ hqfrqwud0vh H +WEQ , @ 57=55 txh ì edvwdqwh lqihulru dr qýphur

revhuydgr 64 vxjhulqgr txh xp pdlru qýphur gh frqjorphudgrv irl revhuydgr gr

txh r ydoru hvshudgr vre d klsöwhvh qxod1 Lqihol}phqwh/ d ydulåqfld gh WEQ qær

srgh vhu fdofxodgd mä txh dv yduläyhlv Lm qær vær lqghshqghqwhv1 Hqwuhwdqwr/ xp

whvwh gh klsöwhvh srgh vhu hihwxdgr edvhdqgr0vh qd glvwulexlêær gd hvwdwðvwlfd WEQ

Page 104: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8141 WHVWHV JHQÌULFRV <<

sru vlpxodêær gh Prqwh Fduor xvdqgr r vhjxlqwh dojrulwpr=

41 Jhuh V frqmxqwrv gh gdgrv lqghshqghqwhphqwh/ rqgh fdgd uìsolfd dohdwöuld

srvvxl r phvpr qýphur gh fdvrv F txh r frqmxqwr gh gdgrv ruljlqdo1 Hvwhv F

fdvrv vær glvwulexðgrv dr dfdvr hqwuh dv q äuhdv gh dfrugr frp d klsöwhvh qxod1

Lvwr ì/ hohv vær rewlgrv frpr uhdol}dêøhv gh xpd glvwulexlêær pxowlqrpldo

P+F>�4> ===> �q, rqgh �m @ Qm@S

mQm/ sursruflrqdo d srsxodêær gh fdgd

äuhd1

51 Hp fdgd xp grv V frqmxqwrv gh gdgrv jhudgrv/ urgh wrgr r surfhglphqwr gh

Ehvdj h Qhzho h fdofxoh d hvwdwðvwlfd WEQ rewhqgr W4> ====> WV 1

61 Rughqh r ydoru gh WEQ gr frqmxqwr gh gdgrv ruljlqdo h grv V frqmxqwrv

vlpxodgrv1 Ghqrwh r srvwr gd hvwdwðvwlfd WEQ dvvrfldgd dr frqmxqwr gh gdgrv

ruljlqdo sru U1 Vh U hvwlyhu hqwuh rv 433+4 � �,( pdlruhv srvwrv/ uhmhlwh d

klsöwhvh qxod dr qðyho gh vljql�fåqfld �1 R s0ydoru dvvrfldgr frp hvwh whvwh

ì 4�U@+V . 4,1

Xvdqgr <<< uìsolfdv/ Wxuqexoo hw do +4<<7, hqfrqwududp xp s0ydoru gh 314; sdud

n @ ; h WEQ @ 64 qrv gdgrv gh Qryd \run1 Lvwr lqglfd txh qær kä hylgíqfld gh

frqjorphudgrv qhvwhv gdgrv gh Qryd \run xwlol}dqgr hvwh whvwh jhqìulfr1 Revhuyh

txh qhqkxpd lqirupdêær vreuh dv srvlêøhv grv ghsövlwrv gh ol{r irl xwol}dgd qhvwh

whvwh1

Hperud hvwh whvwh edvhdgr qd hvwdwðvwlfd WEQ vhmd h{wuhpdphqwh ýwlo hoh qær

dmxgd d lghqwl�fdu txdlv vær rv frqjorphudgrv vljql�fdwlyrv txh ghyhuldp vhu dqdo0

lvdgrv1 Hp sulqfðslr/ srghuðdprv shqvdu hp xvdu dtxhohv ghqwuh rv frqwdgrv hp

WEQ txh wlyhudp rv phqruhv �m 1 Qr hqwdqwr/ qær vdehprv txdqwrv ghvvhv frq0

vlghudu h wdpeìp vdehprv txh r s0ydoru ghshqgh gr wdpdqkr gd srsxodêær vre

frqvlghudêær +yhu Fdsðwxor 5,1

Dv ydqwdjhqv h ghvydqwdjhqv gr pìwrgr gh Ehvdj h Qhzho vær dv vhjxlqwhv=

Hoh hvwdelol}d pdlv dv hvwdwðvwlfdv gh whvwh orfdlv> Frqwlqxd r sureohpd gh whvwhv

vlpxowåqhrv h sruwdqwr r pìwrgr ì h{sorudwöulr wdpeìp> Ì ylvxdophqwh djudgäyho

frpr r JDP> H/ frpr JDP/ lghqwl�fd rv frqjorphudgrv1

Page 105: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

433 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

81416 Dgdswdêær gr pìwrgr gh Fx}lfn h Hgzdugv

Fx}lfn h Hgzdugv +4<<3, �}hudp xpd sursrvwd txh wudedokd frp xpd dprvwud

gh fdvrv h rxwud gh frqwurohv vre d irupd gh xp surfhvvr srqwxdo1 Hvwd sursrvwd

srgh vhu idflophqwh dgdswdgd sdud wudedokdu frp gdgrv gh äuhd frpr prvwudprv

d vhjxlu/ uhsuhvhqwdqgr xpd shtxhqd yduldêær hp uhodêær drv whvwhv sursrvwrv sru

Ehvdj h Qhzho +4<<4, h sru Wxuqexoo hw do1 +4<<3,1 Frpr Ehvdj h Qhzho +4<<4,/

hohv frphfdp �{dqgr r qýphur gh fdvrv u1 D vhjxlu/ hp wruqr gr fhqwuölgh gh

fdgd äuhd l txh srvvxl shor phqrv xp fdvr/ wudfh xp fðufxor txh ydl vh h{sdqglqgr

vhx udlr dwì txh r fðufxor frqwhqkd xpd srsxodêær sdud d txdo hvshudprv revhuydu

u hyhqwrv1 D vhjxlu/yhul�txh txdqwrv hyhqwrv Rl irudp gh idwr revhuydgrv h fdofxoh

hqwær

Xu @

q[l@4

+Rl � u, L^|lA3`

Fx}lfn h Hgzdugv ghulydudp dv iöupxodv grv prphqwrv ghvwd hvwdwðvwlfd vre

d klsöwhvh qxod h prvwududp txh hod srvvxl xpd glvwulexlêær dvvlqwrwlfdphqwh

qrupdo srvvlelolwdqgr dvvlp uhdol}du xp whvwh1 Hqwuhwdqwr/ uhfrphqgdprv txh

vhmd ihlwr xp whvwh edvhdgr qd glvwulexlêær gh Prqwh Fduor rewlgd vlpxodqgr V

sdguøhv rewlgrv dwudyìv gd glvwulexlêær pxowlqrpldo1

Hvwh whvwh dsuhvhqwd dv phvpdv ydqwdjhqv h ghvydqwdjhqv gdtxhoh whvwh sur0

srvwr sru Ehvdj h Qhzho +4<<4, pdv qær h{lvwh hvwxgr frpsdudwlyr hqyroyhqgr

hvwh pìwrgr1

81417 Pìwrgr gh Yduuhgxud gh Nxoogrui

Nxoogrui h Qdjduzdood +4<<8, h Nxoogrui +4<<:, dsuhvhqwdudp xp pìwrgr txh

shuplwh uhvroyhu r sureohpd gh whvwhv vlpxowåqhrv gh irupd edvwdqwh hohjdqwh

hqyroyhqgr xp qýphur pðqlpr gh sduåphwurv qær fuxfldlv sdud vhuhp hvfroklgrv

shor xvxäulr1 Hoh srvvxl yäuldv h{whqvøhv h hvwä lpsophqwdgr qr vriwzduh VdWVfdq/

glvsrqðyho judwxlwdphqwh qd lqwhuqhw qr hqghuhêr

kwws = @@gfs=qfl=qlk=jry@EE@VdWVfdq=kwpo

Page 106: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8141 WHVWHV JHQÌULFRV 434

Ydprv dgrwdu d phvpd qrwdêær gh Nxoogrui h Qdjuzdood +4<<8, hperud hod

�txh xp srxfr frqixvd/ dv yh}hv1 Vhmd Q r qýphur wrwdo gh lqglyðgxrv qd srs0

xodêær hp ulvfr h F r qýphur wrwdo gh fdvrv revhuydgr qd uhjlær gh hvwxgr1 D

dqäolvh ì ihlwd frqglflrqdophqwh qr qýphur wrwdo gh fdvrv h dvvlp F ì wudwdgr

frpr xpd frqvwdqwh frqkhflgd1

Ghqrwh sru ] r frqmxqwr gdv äuhdv } fdqglgdwdv d irupduhp xp frqjorphudgr1

Hvwhv fdqglgdwrv } vær rv fðufxorv gh udlr u duelwuäulr fhqwudgrv hp fdgd xp grv q

fhqwuölghv {l1 Hp whvh/ h{lvwh xp qýphur lq�qlwr gh wdlv fðufxorv pdv/ qd suäwlfd/

hvwhv fðufxorv srghp vhu uhvwulwrv dshqdv dtxhohv fhqwudgrv hp {l h frp udlrv ljxdlv

dv glvwåqfldv hqwuh {l h rv ghpdlv fhqwuölghv1 D ud}dr ì txh fðufxorv frp udlrv

oljhludphqwh glihuhqwhv yær frqwhu/ hp jhudo/ dv phvpdv äuhdv h sruwdqwr gh�qhp

r phvpr srvvðyho frqjorphudgr1 R qýphur gh fðufxorv } 5 ] srgh vhu dlqgd

pdlv uhgx}lgr vh frorfduprv xp olplwh qr udlr gh prgr txh qhqkxp fdqglgdwr

d frqjorphudgr } frqwhqkd pdlv gr txh xpd fhuwd srufhqwdjhp/ wdo frpr 53(/

gd srsxodfçr wrwdo gd äuhd1 D�qdo/ qær id} vhqwlgr sursru xp frqjorphudgr txh

frqwhqkd 83(gd srsxodêær wrwdo1

R whvwh gh yduuhgxud gh Nxoogrui ì edvhdgr qr pìwrgr gh pä{lpd yhurvvlplo0

kdqfd1 R sduåphwur qhvwh fdvr ì +}> s> u, rqgh } ghqrwd r fðufxor hp ]/ srvvlyho0

phqwh sdudphwul}dgr shor vhx udlr h frrughqgdv gr fhqwur/ s ì d suredelolgdgh

gh txh xp lqglyðgxr txdotxhu ghqwur gh } vhmd xp fdvr hqtxdqwr txh u ì d phv0

pd suredelolgdgh irud gh }1 D klsöwhvh gh lqwhuhvvh txh rv dxwruhv frqvlghudp

ì txh h{lvwh xpd ýqlfd }rqd } wdo txh s A u1 Lvwr ì/ d klsöwhvh dohwuqdwlyd ì=

K4 = } 5 ]>s A u=D klsöwhvh qxod ì txh K3 = s @ u/ d dohdwrulhgdgh frpsohwd frp

fdgd lqglyðgxr vhqgr ljxdophqwh suryäyho gh vh wruqdu xp fdvr1

Vhmd q} r qýphur gh lqglyðgxrv qd }rqd }/ vhmd F} d yduläyho dohdwöuld ghqr0

wdqgr r qýphur gh fdvrv qd }rqd } h vhmd f} r qýphur revhuydgr gh F} qrv gdgrv1

D ixqêær gh orj0yhurvvlplokdqfd sdud r sduåphwur +}> s> u, ì gdgd sru

O+}> s> u, @ sf} +4� s,

+q}�f} ,u+F�f},+4� u,

+Q�q}�F.f},

R ydoru gr sduåphwur txh pd{lpl}d hvwd ixqêær qær ì qhfhvvduldphqwh dtxhoh

fruuhvsrqghqgr dr fðufxor frp d pdlru wd{d es @ f}@q} qhp dtxhoh frp r pdlru

Page 107: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

435 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

qýphur gh fdvrv f}1 D ud}ær gh yhurvvlplokdqfd ì

� @vxs}5]>sAu O+}> s> u,

vxss@u O+}> s> u,> s> u 5 ^3>4`

R ghqrplqdgru ghvwd ud}ær ì vlpsohvphqwh

vxs

s5+3>4,

sF+4� s,

Q�F@

FF+Q � F,

Q�F

QQ@ O3

r txdo qær ghshqgh gd }rqd } qhp gd glvwulexlêær hvsdfldo grv fdvrv pdv dshqdv

gr qýphur wrwdo gh fdvrv1

R qxphudgru gd ud}ær gh pä{lpd yhurvvlplokdqfd � ì rewlgr hp gxdv hwdsdv

gh pd{lpl}dêær vxfhvvlydv=

vxs

}5]>sAu

O+}> s> u, @ vxs

}5]

vxssAt

O+}> s> t,

Lvwr ì/ �{dprv } 5 ] h hqfrqwudprv d vroxêær s+}, h u+}, txh pd{lpl}d d

yhurvvlplokdqfd h/ d vhjxlu/ wudedokdprv frp O+}> s+},> u+},, sdud rewhu d vroxêær

txh pd{lpl}d hp }1 Dvvlp/ sdud xp srvvðyho fdqglgdwr d frqjorphudgr }/ whprv

O+}> s+},> u+},, @ vxssAu

sf} +4� s,

+q}�f},u+F�f} ,+4� u,

+Q�q}�F.f},

fxmd vroxêær ì gdgd sru�f}q}

�f} �q}�f}q}

�q}�f} �F�f}Q�q}

�F�f} �Q�q}�F.f}

Q�q}

�Q�q}�F.f}> vh f}

q}A

F�f}Q�q}

FF+Q�F,Q�F

QQ > vh f}q}� F�f}

Q�q}

D vhjxlu/ r frqjorphudgr pdlv yhurvvðplo ì dtxhod }rqd e} sdud d txdoO+}> s+},> u+},,ì pd{lpl}dgd= O+e}> s+e},> u+e},, � O+}> s+},> u+},, sdud wrgr } 5 ]1

D glvwulexlêær gh � ghshqgh gd glvwulexlêær gd srsxodêær h ì yluwxdophqwh

lpsrvvðyho gh vhu rewlgd dqdolwlfdphqwh1 Doìp glvwr/ d dsur{lpdêær dvvlqwöwlfd

xvxdo sru xpd glvwulexlêær txl0txdgudgr gd wudqvirupdêær �5 orj� qær ì yäolgd

srlv dv frqglêøhv gh uhjxodulgdgh qær vær vdwlvihlwdv1 Dvvlp/ d vdðgd sursrvwd

sru Nxoogrui h Qdjduzdood +4<<8, ì xwlol}du xp surfhglphqwr gh vlpxodêær Prqwh

Fduor sdud rewhu d glvwulexlêær h{dwd gh � frqglflrqdgd qr qýphur wrwdo gh fdvrv

revhuydgr F1 R dojrulwpr ì r vhjxlqwh=

Page 108: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8141 WHVWHV JHQÌULFRV 436

41 Jhuh V frqmxqwrv gh gdgrv lqghshqghqwhphqwh/ rqgh fdgd uìsolfd dohdwöuld

srvvxl r phvpr qýphur gh fdvrv F txh r frqmxqwr gh gdgrv ruljlqdo1 Hvwhv F

fdvrv vær glvwulexðgrv dr dfdvr hqwuh dv q äuhdv gh dfrugr frp d klsöwhvh qxod1

Lvwr ì/ hohv vær rewlgrv frpr uhdol}dêøhv gh xpd glvwulexlêær pxowlqrpldo

P+F>�4> ===> �q, rqgh �m @ Qm@S

mQm/ sursruflrqdo d srsxodêær gh fdgd

äuhd1 Dowhuqdwlydphqwh/ �m ì sursruflrqdo dr qýphur hvshudgr gh hyhqwrv hp

fdgd äuhd/ fdvr yduläyhlv gh frqixqglphqwr +wdlv frpr lgdgh h vh{r, hvwhmdp

vhqgr xvdgdv1

51 Hp fdgd xp grv V frqmxqwrv gh gdgrv jhudgrv/ fdofxoh d hvwdwðvwlfd gr whvwh

gd ud}ær gh yhurvvlplokdqfd rewhqgr �4> ====> �V 1

61 Rughqh r ydoru gh � gr frqmxqwr gh gdgrv ruljlqdo h grv V frqmxqwrv vlp0

xodgrv1 Ghqrwh r srvwr gd hvwdwðvwlfd � dvvrfldgd dr frqmxqwr gh gdgrv

ruljlqdo sru U1 Vh U hvwlyhu hqwuh rv 433+4 � �,( pdlruhv srvwrv/ uhmhlwh d

klsöwhvh qxod dr qðyho gh vljql�fåqfld �1 R s0ydoru dvvrfldgr frp hvwh whvwh

ì 4�U@+V . 4,1

71 Fdvr d klsöwhvh qxod whqkd vlgr uhmhlwdgd/ vdoyh d }rqd e} dvvrfldgd frp r

pä{lpd yhruvvlplokdqfd gr prghor qær qxor1 Hvwh ì r frqjorphudgr pdlv

yhurvvðplo1

Sdud r prghor hp txh rv gdgrv srvvxhp glvwulexlêær gh Srlvvrq/ vhmd H +�,

r qýphur gh fdvrv hvshudgr hp � vre r prghor qxor +jhudophqwh/ H +�, @ �Q�

rqgh Q� ì r qýphur gh shvvrdv0dqr ghqwur gr fdqglgdwr d frqjorphudgr �,1

Hqwær

O +�,

O3

@

�R�

H+�,

�R� �F �R�

P �H+�,

�F�R�vh R� A H +�,/ h 4 fdvr frqwuäulr1

R whvwh edvhdgr qd hvwdwðvwlfd gh yduuhgxud hvsdfldo srvvxl dv vhjxlqwhv ydqwd0

jhqv=

� ohyd hp frqwd d ghqvlgdgh srsxodwlrqdo qær frqvwdqwh qd uhjlær h wdpeìp

txdotxhu qýphur gh yduläyhlv gh ulvfr frqkhflgdv wdlv frpr lgdgh h vh{r1

Page 109: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

437 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

� Surfxud frqjorphudgrv vhp hvshfl�fdu gh dqwhpær vxd orfdol}dêær h wdpdq0

kr1

� Vh d klsöwhvh qxod ì uhmhlwdgd/ r whvwh iruqhfh d orfdol}dêær gr frqjorphudgr

pdlv yhurvvðplo txh ohyrx d uhmhlêær1

� Hylwd r sureohpd gh whvwh pýowlsorv iruqfhqgr xp s0ydoru uhdo1 Hvwd ì vxd

sulqflsdo ydqwdjhp1

Dv ghvydqwdjhqv gr whvwh gh yduuhgxud hvsdfldo vær dv vhjxlqwhv=

� R pìwrgr �{d d irupd jhrpìwulfd grv fdqglgdwrv d frqjorphudgrv frpr fðu0

fxorv +rx/ dowhuqdwlydphqwh/ dojxpd rxwud irupd vlpsohv wdo frpr holsvhv rx

uhwåqjxorv,1 Lvwr whqgh d fuldu frqjorphudgrv frpsdfwrv hqjoredqgr pxlwdv

yh}hv äuhdv txh/ gh idwr/ qær id}hp sduwh gr frqjorphudgr1 Dsolfdêøhv ghvwh

pìwrgr hp Ehor Krul}rqwh dsuhvhqwdudp hvwh sureohpd gh irupd edvwdqwh

fodud1

� Rpìwrgr ghyh whu xp srghu edl{r frqwud dowhuqdwlydv frp xp judqgh qýphur

gh shtxhqrv foxvwhuv orfdol}dgrv hp srvlêøhv edvwdqwh glihuhqwhv1

815 Whvwhv irfdgrv

Rv whvwhv irfdgrv vær dtxhohv hp txh/ dqwhv gh revhuydu rv gdgrv/ lghqwl�fdp0vh n

srvlêøhv qr pdsd txh vær irqwhv vxvshlwdv gh dxphqwdu r ulvfr hp vxd yl}lqkdqêd1

D klsöwhvh qxod ì d phvpd gh dqwhv pdv djrud d dowhuqdwlyd ì pdlv suhflvdphqwh

hvshfl�fdgd h/ sdud hvwh sureohpd gh whvwhv irfdgrv gh frqjorphudgrv/ ì srvvðy0

ho gh�qlu whvwhv pdlv srghurvrv gr txh dtxhohv dsuhvhqwdgrv dqwhulruphqwh sdud

whvwhv gh frqjorphudgrv jhqìulfrv1 Gh idwr/ d h{shulíqfld gh vdýgh sýeolfd whp

prvwudgr txh h vlwxdêøhv gh yljloåqfld +vxuyhloodqfh,/ xp edl{r srghu ì d w÷qlfd1

Xpd irupd wðslfd gh dxphqwdu r srghu hp whvwhv hvwdwðvwlfrv ì uhgx}lu r frqmxqwr

gh dowhuqdwlydv h surfxudu hvwdwðvwlfdv gh whvwh txh vhmdp srghurvdv frqwud hvwh frq0

mxqwr uhgx}lgr gh dowhuqdwlydv1 Uhgx}lqgr r srghu frqwud dowhuqdwlydv lpsuryäyhlv

rx vhp lqwhuhvvh suäwlfr/ xp pdlru srghu srgh vhu rewlgr frqwud dv dowhuqdwlydv

txh shupdqhfhp gh lqwhuhvvh1

Page 110: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8151 WHVWHV IRFDGRV 438

Jhudophqwh/ rv whvwhv irfdgrv surfxudp yhul�fdu vh r ulvfr dxphqwd frp d

sur{lplgdgh gd irqwh vxvshlwd1 D gl�fxogdgh wìfqlfd qhvwh sureohpd ì txh qær

ì frqkhflgd d irupd ixqflrqdo gd uhodêær hqwuh ulvfr h glvwåqfld ã irqwh1 Vwrqh

+4<;;, surs÷v xp whvwh txh qær ghshqgh gr frqkhflphqwr ghvwd irupd ixqflrqdo1

Frpr dqwhv/ d klsöwhvh qxod ì txh wrgdv dv shvvrdv srvvxhp r phvpr ulvfr gh

vhu xp fdvr/ lqghshqghqwhphqwh grv rxwurv fdvrv h gd srvlêær gh vxd uhvlgíqfld1

Pdlv hvshfl�fdphqwh/ vxsøh0vh txh |l �Srlvvrq+Hl, rqgh/ qr fdvr pdlv vlpsohv/

Hl @ �Ql/ frp Ql ljxdo dr qýphur gh shvvrdv hp ulvfr qd äuhd l h � ì d wd{d

joredo qd uhjlær hp hvwxgr1 Ì frpxp txh � vhmd hvwlpdgr d sduwlu grv suösulrv

gdgrv frprS

|l@S

Ql frp d yduldelolgdgh uhvxowdqwh vhqgr ljqrudgd d vhjxlu1

Qdv vlwxdêøhv frp pdlv lqirupdêær/ r ydoru gh Hl ì fdofxodgr dmxvwdqgr0vh sru

idwruhv gh ulvfr frqkhflgrv h glihuhqwhv hqwuh dv äuhdv/ wdlv frpr lgdgh h vh{r1

D klsöwhvh dowhuqdwlyd djrud ì txh r ulvfr dxphqwd frp d sur{lplgdgh gh orfdlv

suì0hvshfl�fdgrv pdv vhp hvwdeohfhu txdo d irupd ixqflrqdo ghvwh dxphqwr1

R sureohpd gd hvfdod ì xp dvshfwr suäwlfr lpsruwdqwh qhvwhv hvwxgrv1 Xp

frqjorphudgr ì vhphokdqwh d xp rxwolhu qxp hvwxgr hvwdwðvwlfr1 Xpd revhuydêær

ì frqvlghudgd xp rxwolhu qr frqwh{wr gh xpprghor hvwdwðvwlfr1 Gr phvpr prgr/ d

qrêær gr txh ì xp frqjorphudgr ghshqgh gdv uhjlær vre frqvlghudêær1 Xpd uhjlær

pxlwr judqgh idwdophqwh vhuä khwhurjíqhd hp dvshfwrv txh hvwær uhodflrqdgrv frp

rv ulvfr pdv txh qær hvwær glvsrqðyhlv1 Ì frpxp dwì txh judqghv glihuhqfdv

uhjlrqdlv hp wd{dv vhmdp uhodflrqdgdv d glihuhqfdv qd frehuwxud gr uhjlvwur gh

fdvrv1 Dvvlp/ rv hvwxgrv gh frqjorphudgrv wudedokdp frp uhjløhv uhodwlydphqwh

krprjíqhdv h yduldqgr hqwuh 43 h 58 np gh udlr hp wruqr gr vxsrvwr irfr1 Qr

Uhlqr Xqlgr/ rv hvwxgrv gd Vpdoo Duhd Khdowk Vwdwlvwlfv Xqlw xvdp xp udlr gh 43

np hp wruqr gdv irqwhv vxvshlwdv frpr vhqgr d uhjlær gh hvwxgr1

H{dpsoh 46 Qr h{hpsor gh Wxuqexoo hw do1 +4<<7,/ 45 orfdlv vær srvvðyhlv irqwhv

gh frqwdplqdêær1 Hvwhv orfdlv vær rv ghsövlwrv gh ol{r wö{lfr frqwdplqdgrv shor

frpsrvwr rujåqflr yroäwlo wulforurhwlohqr +WFH,1 Hvwh frpsrvwr frqwdplqd r vror

h whp vlgr dvvrfldgr frp lqflgíqfld gh ohxfhpld/ hperud d hylgíqfld vhmd iudfd1

Ohqfölv gh äjxd frqwdplqdgd iuhtxhqwhphqwh frqwhp WFH ehp frpr rxwurv frp0

Page 111: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

439 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

srvwrv fxmr hihlwr fdqfhuðjhqr ì pdlv frqkhflgr1 Dvvlp/ d suhvhqfd gh WFH irl

frqvlghudgr xpd sur{| sdud d h{srvlêær d frpsrvwrv fdqfhuðjhqrv hp jhudo qr

vror

H{dpsoh 47 Hoolrww hw do1 +4<<9, hvwxgdudp d lqflgíqfld gh fåqfhu gr hvw÷pdjr

dr uhgru gh lqflqhudgruhv pxqlflsdlv gh ol{r vöolgr1 Rv gdgrv frqvlvwhp gr qýphur

gh fdvrv gh fåqfhu gh hvw÷pdjr hp fdgd Glvwulwr gh Hqxphudêær +Hqxphudwlrq

Glvwulfw/ hp lqjoív,/ txh vær vlploduhv drv Vhwruhv Fhqvlwäulrv eudvlohlurv1 Doìp

ghvwdv revhuydêøhv dohdwöuldv/ hohv wdpeìp srvvxldp r qýphur hvshudgr gh fdvrv

sdgurql}dgr sru lgdgh h vh{r h xp ðqglfh gh txdolgdgh gh ylgd fkdpdgr Fduvwdluv1

81514 Dgdswdêær grv pìwrgrv dqwhulruhv

Xpd irupd vlpsohv gh dwdfdu hvwh sureohpd ì dgdswdu dojxqv grv pìwrgrv dqwh0

ulruhv gh whvwh jhqìulfrv d hvwh sureohpd gh whvwhv irfdgrv1 Dvvlp/ Ehvdj h Qhzho

+4<<4, sursxvhudp ghwhuplqdu d uhjlær qhfhvväuld sdud rewhu shor phqrv u fdvrv

hp wruqr dshqdv gdv irqwhv vxvshlwdv1 Vh dv irqwhv qær iruhp pxlwdv/ r hihlwr

gh whvwhv vlpxowåqhrv srghp vhu frqwurodgrv dwudyìv gh surfhglphqwrv vlpsohv

wdlv frpr fruuhêøhv gh Erqihuurql1 Hperud dwudwlyr/ hvwh surfhglphqwr vriuh gd

ghvydqwdjhp gh ljqrudu d glvwåqfld dwì d irqwh dr frqvlghudu gr phvpr prgr hp u

rv fdvrv pxlwr suö{lprv gd irqwh h dtxhohv xp srxfr pdlv didvwdgrv1 Doìp glvwr/

hoh qhfhvvlwd gd ghwhuplqdêær gh u dqwhv gh revhuydu rv gdgrv r txh qhp vhpsuh ì

iäflo gh vhu ihlwr1 Hp jhudo/ u ì hvfroklgr gh irupd lqwxlwlyd ohydqgr0vh hp frqwd d

ghqvlgdgh srsxodflrqdo h d hvfdod qd txdo rv frqjorphudgrv vær dqwhflsdgdphqwh

hvshudgrv1 Qr hqwdqwr/ xpd hvfrokd pdo ihlwd gr ydoru gh u/ xp u pxlwr pdlru

gr txh r qhfhvväulr/ sru h{hpsor/ srgh ohydu d qær ghwhfêær gh xp frqjorphudgr

shtxhqr txh dsduhfh vxephuvr qxpd uhjlær pdlru txh irl qhfhvväulr dfxpxodu hp

wruqr gd irqwh1

H{dpsoh 48 Xvdqgr rv gdgrv gh Qryd \run/ srgh0vh fdofxodu r s0ydoru dvvrfldgr

frp fdgd xp grv 45 orfdlv rqgh kä ghsövlwr frp WFH xwlol}dqgr u @ 9> ;> 43 +yhu

Wdehod 815,1 Dshqdv grlv orfdlv srvvxhp s0ydoru phqru txh 3138/ xp irfr txdqgr

n @ 9 h rxwur irfr txdqgr n @ 431 Rv grlv irfrv irudp glihuhqwhv1 Dvvlp/ hvwh

Page 112: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8151 WHVWHV IRFDGRV 43:

Irfr u @ 9 u @ ; u @ 43

Prqdufk 3139< 313:5 31346

LEP 3155: 31389 313:5

Vlqjhu 31998 31:58 317:3

Qhvfr 31998 31:58 317:3

JH Dxexuq 3143; 31466 31476

Vroyhqw Vdyhuv 31884 31587 3149;

Vplwk Frurqd 3166: 3158; 31453

Ylfwru| Sod}d 31346 317<5 3156:

Kdgfr 31:9< 317<3 315;7

Pruvh Fkdlq 31;76 31:59 31;:<

Jurwrq 31;7: 31;:8 31:55

Whvwh Joredo 31648 31935 31667

Wdehod 815= Wdehod frp rv uhvxowdgrv gh dsolfdêær gr whvwh gh Ehvdj h Qhzho frp

n @ 9> ;>43 qrv gdgrv gh ohxfhpld qr qruwh gr hvwdgr gh Qryd \run +Zdoohu hw do1/

4<<5,1

pìwrgr qær hqfrqwud hylgíqfld vx�flhqwh qrv gdgrv sdud d�upduprv txh h{lvwh

hihlwr gh dxphqwr gh ulvfr dr uhgru gdv irqwhv1 R whvwh joredo ì edvhdgr qd hvwdwðv0

wlfd WEQ h vhx s0ydoru irl fdofxodgr xvdqgr0vh d glvwulexlêær Prqwh Fduor ghvwd

hvwdwðvwlfd1

81515 Whvwh gh hvfruh

Vhp shugd gh jhqhudolgdgh/ urwxoh dv q äuhdv shod glvwåqfld ã irqwh gh prgr

txh l @ 4 ì d pdlv suö{lpd gd irqwh h l @ q ì d pdlv glvwdqwh1 Vxsrqkd txh

dv revhuydêøhv vær dv frqwdjhqv |l �Srlvvrq+�lHl, h txhS

l |l @ F1 Vxsrqkd

txh rv ulvfrv uhodwlyrv gh fdgd äuhd vær frqkhflgrv vre dv gxdv klsöwhvhv/ qxod h

dowhuqdwlyd/ h vær hvfulwrv frpr �43> �53> ===> �q3 vre d qxod h frpr �44> �54> ===> �q4

vre d dowhuqdwlyd1 R orjdulwpr gd ud}ær gh yhurvvlplokdqfdv vre dv gxdv klsöwhvhv

Page 113: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

43; FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

ì gdgr sru

orjO @

q[l@4

^|l orj +�l4@�l3,�Hl +�l4 � �l3,`

Sdud ydoruhv �{rv h frqkhflgrv grv ulvfrv/ r vhjxqgr whupr dflpd ì frqvwdqwh h

sruwdqwr/ shor ohpd gh Qh|pdq h Shduvrq/ r whvwh pdlv srghurvrv gh K3 yhuvxv

K4 ì gd irupd

W @

q[l@4

|l orj +�l4@�l3, A f

sdud dojxpd frqvwdqwh f1 Dvvxplqgr txh/ sdud wrgr l/ �l3 @ �3/ ghvfrqkhflgr/ r

phokru whvwh ì gdgr sru

W @

q[l@4

|l orj �l4 �q[l@4

|l orj�3 A f

Vh rv ydoruhv hvshudgrv irudp fdofxodgrv gh wdo irupd txh srghprv dvvxplu

�3 @ 4/ hqwær r whvwh dflpd ì idflophqwh fdofxodgr txdqgr frqkhfhprv rv ydoruhv

�l41 Qr hqwdqwr/ pxlwdv yh}hv/ �3 ì ghvfrqkhflgr srlv rv ydoruhv hvshudgrv srghp

whu vlgr fdofxodgrv xvdqgr0vh ydoruhv gh xpd uhjlær pxlwr pdlru/ wdo frpr xp hv0

wdgr rx wrgr r sdðv/ txh d hvwxgdgd1 D ud}ær sdud lvwr vhuä r shtxhqr qýphur gh

fdvrv gd uhjlær hvwxgdgd sdud hihwxdu xpd sdgurql}dêær lqgluhwd1 Hqwuhwdqwr/ fr0

pr F ì hvwdwðvwlfd dqflodu sdud �l4/ d dqäolvh dsursuldgd ì frqglflrqdu qr hvwlpdgru

gh pä{lpd yhurvvlplokdqfd f�3 @ F@S

lHl h xvdu d ud}ær gh orj0yhurvvlplokdqfd

edvhdgd qd glvwulexlêær pxowlqrpldo

W @

q[l@4

|l orj�l4 �F orj

��l4HlS

Hl

�rqgh r vhjxqgr whupr ì xpd frqvwdqwh1 Lvwr ì htxlydohqwh sruwdqwr d wudedokdu

frp xp whvwh edvhdgr qd vrpd srqghudgd gh wrgrv rv fdvrv xvdqgr frpr shvr

xp hvfruh txh ì d wd{d �l4 gd äuhd gh uhvlgíqfld grv fdvrv1

Hqwuhwdqwr/ rv ydoruhv �l4 xvxdophqwh qær vhuær frqkhflgrv1 H{lvwh d dowhuqd0

wlyd gh lpsru xpd irupd sdudpìwulfd d hvwhv ulvfrv uhodwlyrv pdv lvwr qær ì xpd

hvwudwìjld pxlwr dgrwdgd1 D ud}ær ì txh qær h{lvwhp hohphqwrv vx�flhqwhv sdud

dvvxplu hvwd irupd sdudpìwulfd h/ hp jhudo/ F h fdgd |l vhuä pxlwr shtxhqr sdud

Page 114: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8151 WHVWHV IRFDGRV 43<

shuplwlu xpd erd hvwlpdêær gh sduåphwurv txh prghohp r hihlwr gh irqwh txh qær

ghyh vhu pxlwr judqgh1

Hqwuhwdqwr/ hvwd dqäolvh ohyrx foävvlfd prwlyrx Zdoohu hw do1 +4<<5, h Odz0

vrq +4<<6, txh/ lqghshqghqwhphqwh sursxvhudp r phvpr whvwh orfdophqwh pdlv

srghurvr edvhdgr qd hvwdwðvwlfd hvfruh frqvlghudqgr d vhjxlqwh sduwlfxodu klsöwhvh

dowhuqdwlyd=

K4 = �4l @ 4 . �jl

rqgh � ì xpd frqvwdqwh srvlwlyd pdv ghvfrqkhflgd h jl vær frqvwdqwhv frqkhflgdv

h uhsuhvhqwdqgr sur{lhv sdud d h{srvlêær qd äuhd l1 Ì frpxp/ sru h{hpsor/ wrpdu

jl @ 4@gl rx jl @ h{s +�gl@N, rqgh gl ì d glvwåqfld gr fhqwuölgh gd äuhd l dwì d

irqwh h N ì �{r h frqkhflgr1 Qrwh txh hvwh ì xp prghor frp ýqlfr sduåphwur/ �/

h txh d klsöwhvh qxod fruuhvsrqgh d vlwxdêær hp txh � @ 31 R srqwr lpsruwdqwh

ì txh d hvwdwðvwlfd gr whvwh gh hvfruh orfdophqwh pdlv srghurvr qær ghshqgh gh �=

W @C orjO

C�m�@3 @

q[l@4

jl+|l �Hl,

Dvvlp/ hvwhv dxwruhv sursxvhudp r whvwh edvhdgr qd hvwdwðvwlfd W gh�qlgd dfl0

pd txh/ vre d klsöwhvh qxod/ srvvxl hvshudqêd ljxdo d }hur h ydulåqfld ljxdo d

lqirupdêær gh Ilvkhu/ txh ì dsur{lpdgdphqwh ljxdo d

Ydu+W , �q[l@4

j5lHl

D hvwdwðvwlfd sdgurql}dgd W� @ X@sS

j5lHl srvvxl glvwulexlêær dvvlqwöwlfdQ+3>4,1

Hvwd dsur{lpdêær ì jhudophqwh pxlwr erd1

Vh yäuldv irqwhv hvwær suhvhqwhv h vær uhodwlydphqwh suö{lpdv/ ì frpxp gh�qlu

jl xvdqgr d phqru glvwåqfld gd äuhd l d fdgd xpd gdv irqwhv suhvhqwhv qd uhjlær1

Ydprv dsuhvhqwdu xp h{hpsor frp rv gdgrv gh Qryd \run qr �qdo gd suö{lpd

vhêær1

81516 Whvwh gh Vwrqh +4<;;,

Vwrqh +4<;;, surs÷v xp whvwh sdud xpd ýqlfd irqwh srqwxdo vxvshlwd txh wruqrx0

vh edvwdqwh srsxodu1 Xp judqgh qýphur gh hvwxgrv gh fdvrv wíp vlgr edvhdgr

Page 115: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

443 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

qhvwh whvwh +Elwkhoo/ 4<<3> Elwkhoo h Vwrqh/ 4<;<> Hoolrww hw do1/ 4<<5> Wxuqexoo hw

do1/ 4<<3> Zdoohu hw do1/ 4<<5/ hqwuh rxwurv,1 Hvwh pìwrgr whp vlgr frqvlghudgr r

phokru whvwh irfdgr sdud gdgrv gh äuhd dwì r prphqwr/ frp dojxpdv dgdswdêøhv

dsuhfhqgr rfdvlrqdophqwh +Pruwrq0Mrqhv hw do1/ 4<<<,1 Hoh ì r pìwrgr suhihulgr

shod lpsruwdqwh djíqfld eulwåqfld Vpdoo Duhd Khdowk Vwdwlvwlfv Xqlw +VDKVX,1

Vhp shugd gh jhqhudolgdgh/ urwxoh dv q äuhdv shod glvwåqfld ã irqwh gh prgr

txh l @ 4 ì d pdlv suö{lpd gd irqwh h l @ q ì d pdlv glvwdqwh1 Vxsrqkd txh dv

revhuydêøhv vær dv frqwdjhqv |l �Srlvvrq+�lHl, h txhS

l |l @ F1 Qhvvh whvwh/ dv

klsöwhvhv qxod h dowhuqdwlyd vær dv vhjxlqwhv=

K3= �4 @ �5 @ === @ �q

KD= �4 � �5 � === � �q

D hvwdwðvwlfd gh whvwh ì r pä{lpr gr ulvfr uhodwlyr hvwlpdgr sdud xpd uhjlær

hp wruqr gd irqwh vxvshlwd=

WVwrqh @ pd{4�m�q

Sm

l@4 |lSml@4 Hl

R s0ydoru gr whvwh dvvrfldgr frp r ydoru revhuydgr WVwrqh @ w ì S +WVwrqh A

w, @ 4 � S +WVwrqh � w,>frpr h{solfduhprv dedl{r1 Hperud r whvwh vhmd lqwxlwl0

ydphqwh vlpsohv/ hoh qær ì xp whvwh xqliruphphqwh pdlv srghurvr +XPS, sdud

xp dfuìvflpr gh ulvfr prqöwrqr frp d glvwåqfld d irqwh/ frpr ylprv qd vhêær

dqwhulru1 Hqwuhwdqwr/ ududphqwh ì r fdvr hp txh h{lvwhp gdgrv vx�flhqwhv hp fdgd

äuhd +lvwr ì/ frp shtxhqd ydulåqfld uhodwlydphqwh ã pìgld, sdud txh xpd irupd

sdudpìwulfd hvshfð�fd +wdo frpr xp ghfdlphqwr olqhdu rx h{srqhqfldo d sduwlu gd

irqwh, vhmd dgrwdgr1 Dvvlp/ r whvwh sursrvwr sru Vwrqh +4<;;, frqwlqxd vhqgr xpd

erd vroxêær fdvr qær kdmd lqirupdêær dglflrqdo glvsrqðyho1 Vhmd H r pdlru lqwhlur

phqru rx ljxdo d wSq

l@4 Hl1 Hqwær/

S +WVwrqh � w, @ S

#l[

n@4

|n � w

l[n@4

Hn = l @ 4> ===> q

$@

H[m@3

t+q> m,

h

t+y> m, @ S

##y[

n@4

|n @ m

$_

#l[

n@4

|n � w

l[n@4

Hn = l @ 4> ===> y

$$

Page 116: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8151 WHVWHV IRFDGRV 444

Dv suredelolgdghv t+y=m, vær lqwhusuhwdgdv frpr d suredelolgdgh gh txh dv y

äuhdv pdlv suö{lpdv gd irqwh frqwhqkdp m fdvrv h txh wrgdv dv ud}øhv dfxpxodgdv

dwì y gh fdvrv vreuh qýphur hvshudgr ì phqru txh w1 Hvwdv suredelolgdghv vær

rewlgdv gh irupd uhfxuvlyd d sduwlu gdv htxdêøhv edfnzdug dvvrfldgdv frp xp

sdvvhlr dohdwöulr qr sodqr h/ vre d klsöwhvh qxod/ vær gdgdv sru

t+y> m, @

Sm

n@3 t+y � 4> m � n, h{s +�Hy,Hny@n$> m @ 3> ===>H

3

3> m A H3

frp t+3>3, @ 4 h H3 r pdlru lqwhlur phqru rx ljxdo d wSy

l@4 Hl1

Hvwh surfhglphqwr srgh vhu ylvwr frpr xp phlr gh dmxvwdu r qðyho gh vlj0

ql�fåqfld qrplqdo sru fdxvd gr hihlwr gh vhohflrqdu xpd uhjlær dr uhgru gd irqwh

txh srvvxl r pdlru ulvfr uhodwlyr revhuydgr1

Xp surjudpd gh frpsxwdgru sdud uhdol}du hvwhv fäofxorv srgh vhu rewlgr gl0

uhwdphqwh gr dxwru1 Qr hqwdqwr/ qd suäwlfd/ ì vhpsuh pdlv vlpsohv rewhu d glv0

wulexlêær gd hvwdwðvwlfd gh whvwh sru phlr gh vlpxodêær Prqwh Fduor vre d klsöwhvh

qxod frqglflrqdgd qr qýphur wrwdo F gh fdvrv revhuydgr1

41 Jhuh V frqmxqwrv gh gdgrv lqghshqghqwhphqwh/ rqgh fdgd uìsolfd dohdwöuld

srvvxl r phvpr qýphur gh fdvrv F txh r frqmxqwr gh gdgrv ruljlqdo1 Hvwhv

F fdvrv vær glvwulexðgrv frpr uhdol}dêøhv gh xpd glvwulexlêær pxowlqrpldo

P+F>�4> ===> �q, rqgh �m 2 Hm 1

51 Hp fdgd xp grv V frqmxqwrv gh gdgrv jhudgrv/ fdofxoh d hvwdwðvwlfd gh whvwh

Vwrqh rewhqgr W4> ===> WV / doìp gr ydoru w fdofxodgr frp rv gdgrv ruljlqdlv1

61 Rughqh rv ydoruhv iw> W4> ===> WVj h ghqrwh r srvwr gh w sru U1 VhU hvwlyhu hqwuh

rv 433+4��,(pdlruhv srvwrv/ uhmhlwh d klsöwhvh qxod dr qðyho gh vljql�fåqfld

�1 R s0ydoru dvvrfldgr frp hvwh whvwh ì 4�U@+V . 4,1

Xpd vlpsohv prgl�fdêær gr whvwh ì ihlwd txdqgr h{lvwh pdlv gh xp irfr vxv0

shlwr suhvhqwh qd uhjlær h hvvhv irfrv qær hvwær pxlwr glvwdqwhv hqwuh vl1 Rughqdp0

vh dv äuhdv shodv vxdv glvwåqfldv dr irfr pdlv suö{lpr h dvvlp uhdol}du xp whvwh

vlpxowåqhr gh txh r ulvfr dxphqwd txdqwr pdlv suö{lpd d äuhd hvwä gh txdotxhu

xp gdv irqwhv vxvshlwdv1 Revhuyh txh d dowhuqdwlyd frqvlghudgd dtxl ì txh r ulvfr

Page 117: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

445 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

dxphqwd hp wruqr gh wrgdv dv irqwhv/ hperud qær suhflvh vhu gd phvpd irupd hp

fdgd xpd ghodv1 Qr hqwdqwr/ r whvwh whuä phqrv srghu qd vlwxdêær hp txh dojxpdv

irqwhv dxphqwdp rv ulvfrv hqtxdqwr rxwudv qær r id}hp1

Txdqgr I irfrv hvwær hp srvlêøhv wær vhsdudgdv txh d dqäolvh ì ihlwd vhsd0

udgdphqwh sdud fdgd irfr/ d dowhuqdwlyd sdud rewhu xp s0ydoru djuhjdgr ì fdofxodu

d wudglflrqdo hvwdwðvwlfd sursrvwd sru Ilvkhu1 Qhvwh fdvr/ frpelqdprv rv s0ydoruhv

sn gh fdgd irqwh lqglylgxdo rewhqgr d hvwdwðvwlfd �5S

n orj sn � [ 55I 1

D sulqflsdo frqvlghudêær txh ghyhuld qrv jxldu qd hvfrokd gh xp whvwh dsursul0

dgr ì r vhx srghu uhodwlydphqwh d rxwurv whvwhv fdqglgdwrv frp uhodêær d klsöwhvhv

dowhuqdwlydv gh lqwhuhvvh1 Lqihol}phqwh/ qær h{lvwhp uhvxowdgrv dqdoðwlfrv vreuh r

srghu gd hvwdwðvwlfd WVwrqh 1 D glvwulexlêær qxod srgh vhu dsur{lpdgd sru xpd plv0

wxud gh glvwulexlêøhv txl0txdgudgr pdv frp rv shvrv gd plvwxud ghvfrqkhflgrv1

sduhfh lqhylwäyho txh frqfoxvøhv vhmdp edvhdgdv hp hvwxgrv gh vlpxodêær pdv qær

h{lvwhp uhvxowdgrv frqfoxvlyrv dlqgd1

H{dpsoh 49 Qr h{hpsor gr hvwdgr gh Qryd \run/ dsolfdqgr0vh rv pìwrgrv gh

Vwrqh h gh hvfruh/ hqfrqwudprv rv uhvxowdgrv gd Wdehod 8161 Ilfd fodur txh r whvwh

joredo gh hvfruh ghwhfwrx iruwh hylgíqfld gh txh r ulvfr ì pdlv hohydgr dr uhgru

grv ghsövlwrv gh ol{r hqtxdqwr txh r whvwh gh Vwrqh qær irl fdsd} gh ghwhfwdu hvwh

hihlwr1 Dr phvpr whpsr/ r whvwh gh hvfruh sduhfh vhu pdlv vhqvðyho txh r gh Vwrqh

txdqgr dsolfdgr hp fdgd xp grv orfdlv vhsdudgdphqwh1

816 Frqfoxvøhv

Whvwhv gh frpsdudêær hqwuh hvwhv pìwrgrv/ jhqìulfrv rx irfdgrv/ h{lvwhp pdv hp

jhudo qær vær wrwdophqwh frqfoxvlyrv1 Xpd gdv gl�fxogdghv ì d ghshqgíqfld gd

glvwulexlêær gd hvwdwðvwlfd gh whvwh qd hvwuxwxud gd srsxodêær hp ulvfr/ gd irupd gh

didvwdphqwr gd klsöwhvh qxod/ gr qðyho gd wd{d gh rfruuíqfld gh fdvrv h gd glylvær

sroðwlfd dgrwdgd1 D ghshqgíqfld gh wdqwrv idwruhv pdlv r qýphur pxlwr judqgh

gh whvwhv txh frqwlqxdp vhqgr sursrvwrv/ grv txdlv freulprv dshqdv rv sulqflsdlv/

id} frp txh vxjhvwøhv txdqwr dr whvwh d vhu dgrwdgr pxlwr �uphv vhmdp gliðfhlv gh

vhuhp gdgdv1

Page 118: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8161 FRQFOXVØHV 446

Irfr WVwrqh W�

Prqdufk 31344 ?31334

LEP 31369 ?31334

Vlqjhu 31578 3133:

Qhvfr 31578 3133:

JH Dxexuq 31489 31353

Vroyhqw Vdyhuv 31835 316;9

Vplwk Frurqd 31495 31338

Ylfwru| Sod}d 31435 31357

Kdgfr 318:5 31364

Pruvh Fkdlq 31:;7 31:;5

Jurwrq 316;8 3153<

Whvwh Joredo 3153: ?31334

Wdehod 816= Wdehod frp rv uhvxowdgrv gh dsolfdêær gr whvwh gh Vwrqh h gh hvfruh

qrv gdgrv gh ohxfhpld qr qruwh gr hvwdgr gh Qryd \run +Zdoohu hw do1/ 4<<5,1

Page 119: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

447 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

Xpd gdv frpsdudêøhv pdlv lpsruwdqwhv ihlwdv frp whvwhv gh frqjorphudgrv

jhqìulfrv irl dtxhod uhdol}dgd sru Doh{dqghu h Er|oh +4<<9,1 Hvwhv shvtxlvdgruhv

frqyhqfhudp rv sulqflsdlv dxwruhv grv pìwrgrv sursrvwrv dwì dtxhoh prphqwr d

vxephwhuhp0vh d xp h{shulphqwr1 Rv dxwruhv uhfhehudp xp judqgh qýphur gh

pdsdv rqgh ghyhuldp dsolfdu vhxv pìwrgrv sdud ghwhfwdu srvvðyhlv frqjorphudgrv1

Dojxqv pdsdv qær srvvxldp qhqkxp frqjorphudgr hqtxdqwr txh rxwurv pdsdv

srvvxldp xp qýphur yduläyho gh frqjorphudgrv txh wdpeìp yduldydp hp wdpdq0

kr1 Rv dxwruhv qær vdeldp qdgd vreuh rv pdsdv d qær vhu r surfhglphqwr jhqìulfr

dgrwdgr sdud jhuä0orv1 Hohv hudp olyuhv sdud hvfrokhu gd irupd txh suhihulvvhp

rv sduåphwurv dvvrfldgrv frp vhxv pìwrgrv +wdo frpr r s0ydoru qr fdvr gr JDP

gh Rshqvkdz rx gh Ehvdj h Qhzho,1 Dsöv dsolfdu rv vhxv pìwrgrv/ rv dxwruhv

ghfodudydp vh kdyld frqjorphudgr qr pdsd/ txdqwrv hudp h rqgh hvwdydp1

Yäuldv dqäolvhv grv uhvxowdgrv rewlgrv irudp ihlwdv h/ hperud Doh{dqghu h Er|oh

+4<<9, vhmdp fdxwhorvrv dr vxjhulu frqfoxvøhv/ �fd fodur d sdulu gr h{shulphqwr

txh rv pìwrgrv JDP gh Rshqvkdz h r gh Ehvdj h Qhzho vær rv phokruhv1 Frpr

hvwhv pìwrgrv h{ljhp xpd vìulh gh hvfrokdv gh ydoruhv gh sduåphwurv sdud rv vhxv

dojrulwprv/ hvwd vxshulrgdgh srgh qær vh pdqwhu qdv pærv gh shvvrdv vhp d ghylgd

h{shulíqfld frp rv pìwrgrv h frp r sureohpd frqfuhwr vre dqäolvh1

Gxdv lpsruwdqwhv txdol�fdêøhv vær qhfhvväuldv1 D sulphlud ì qrwdu txh krx0

yh xpd lpsruwdqwh dxvíqfld qd frpsdudêær gh Doh{dqghu h Er|oh +4<<9,/ d gr

pìwrgr gh Nxoogrui h Qdjduzdood +4<<8, txh hvwdyd vhqgr sxeolfdgr mxqwr frp

r olyur dflpd1 Lvwr ì odphqwäyho srlv hvwh pìwrgr ì r ýqlfr txh frqwurod r huur

wlsr L gd irupd fruuhwd1 D rxwud txdol�fdêær gl} uhvshlwr d xpd olplwdêær ghvwh

hvwxgr1 Qær hud gliðflo lpdjlqdu txh/ grv pxlwrv pdsdv d vhuhp dqdolvdgrv/ xpd

sursruêær vxevwdqfldo/ wdoyh} pdlv gh 83( ghohv/ ghyhuldp frqwhu shor phqrv xp

frqjorphudgr1 Dvvlp/ rv dxwruhv txh dqwhflsdudp fruuhwdphqwh hvwh idwr h txh

hqwær lpsolflwdphqwh xvdudp huurv wlsr L pdlv jhqhurvrv whqgldp d vhu idyruhflgrv1

Lvwr ì/ xpd hvfrokd gh xp s0ydoru qær pxlwr shtxhqr sdud fdgd fðufxor whvwdgr

lqglylgxdophqwh vhuld ehqì�fr drv pìwrgrv JDP gh Rshqvkdz h r gh Ehvdj h

Qhzho1

Txdqwr drv whvwhv irfdgrv/ dojxqv hvwxgrv gh srghu whp prvwudgr txh dperv/

Page 120: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

8161 FRQFOXVØHV 448

r whvwh gh Vwrqh h r whvwh gh hvfruh/ vær rv phokruhv whvwhv glvsrqðyhlv +Zdoohu h

Odzvrq/ 4<<8> Zdoohu h Srtxhwwh/ 4<<<,1

Page 121: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

449 FDSÐWXOR 81 WHVWHV GH FRQJORPHUDGRV

Page 122: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

����������

^4` Dqghv/ Q1 h Gdylv/ M1H1 +4<<8, Olqnlqj Sxeolf Gdwd Xvlqj Jhrjudsklfdo Lqiru0

pdwlrq V|vwhpv Whfkqltxhv= Dodvndq Frppxqlw| Fkdudfwhulvwlfv dqg Lqidqw

Pruwdolw|1 Vwdwlvwlfv lq Phglflqh/ 47/ 7;407<31

^5` Doh{dqghu I1H1/ PfNlqqh| S1D1/ Fduwzuljkw U1D1/ h Ulfnhwwv W1M1/ +4<<4,

Phwkrgv ri pdsslqj dqg lghqwli|lqj vpdoo foxvwhuv ri glvhdvh zlwk dssolfdwlrqv

wr jhrjudklfdo hslghplrorj|/ Jhrjudsklfdo Dqdo|vlv/ 56/ 48904:61

^6` Doh{dqghu I1H1 h Er|oh S1 +hgv1, +4<<9, Phwkrgv iru Lqyhvwljdwlqj Orfdolvhg

Foxvwhuv ri Glvhdvh/ LDUF Vflhqwl�f Sxeolfdwlrq 468/ Lqwhuqdwlrqdo Djhqf|

iru Uhvhdufk rq Fdqfhu/ O|rq/ Iudqfh1

^7` Dqghuvrq Q1K1 h Wlwwhulqjwrq G1P1 +4<<:, Vrph phwkrgv iru lqyhvwljdwlqj

vsdwldo foxvwhulqj/ zlwk hslghplrorjlfdo dssolfdwlrqv/ Mrxuqdo Ur|do Vwdwlvwlfdo

Vrflhw|/ Vhulhv D/493/ ;:04381

^8` Dqvholq O1 +4<<8, Orfdo lqglfdwruv ri vsdwldo dvvrfldwlrq�OLVD/ Jhrjudsklfdo

Dqdo|vlv/ 5:/ <604481

^9` Dvvxqêær/ U1 P1 h Jxwwrus/ S1 +4<<<, Urexvwqhvv iru lqkrprhjhqrxv Srlvvrq

srlqw surfhvvhv1 Dqqdov ri wkh Lqvwlwxwh ri Vwdwlvwlfdo Pdwkhpdwlfv/ 84/ 98:0

9:;1

^:` Dvvxqêær U1P1 h Uhlv H1D1 +4<<<, D qhz sursrvdo wr dgmxvw Prudq*v L iru

srsxodwlrq ghqvlw| Vwdwlvwlfv lq Phglflqh/ 4;/ 547:054951

44:

Page 123: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

44; ELEOLRJUDILD

^;` Dvvxqêær U1P1 h Uhlv L1D1 +5334, Gl�xvlrq dqg Suhglfwlrq ri Ohlvkpdqldvlv lq

d Odujh Phwursrolwdq Duhd lq Eud}lo= d Ed|hvldq Vsdfh0Wlph Prgho1 Vwdwlvwlfv

lq Phglflqh/ 53/ d dsduhfhu1

^<` Edloh|/ W1 h Jdwuhoo/ D1 +4<<8, Lqwhudfwlyh Vsdwldo Gdwd Dqdo|vlv/ Orqjpdq

Vflhqwl�f dqg Whfkqlfdo/ Hvvh{1

^43` Ednhu U1G1 +4<<9, Whvwlqj iru vsdfh0wlph foxvwhuv ri xqnqrzq vl}h/ Mrxuqdo

ri Dssolhg Vwdwlvwlfv/ 56/ 87608871

^44` Ehuqduglqhool O1 h Prqwrprol P1 +4<<5, Hpslulfdo Ed|hv yhuvxv ixoo| Ed|hvldq

dqdo|vlv ri jhrjudsklfdo yduldwlrq lq glvhdvh ulvn/ Vwdwlvwlfv lq Phglflqh/ 44/

<;60433:1

^45` Ehuqduglqhool O1/ Fod|wrq G1/ Sdvfxwwr F1/ Prqwrprol F1 h Jklvodqgl P1

+4<<8d, Ed|hvldq dqdo|vlv ri vsdfh0wlph yduldwlrq lq glvhdvh ulvn/ Vwdwlvwlfv

lq Phglflqh/47/ 5766057761

^46` Ehuqduglqhool O1/ Fod|wrq G1 h Prqwrprol F1 +4<<8e, Ed|hvldq Hvwlpdwhv ri

glvhdvh pdsv= krz lpsruwdqw duh sulruvB Vwdwlvwlfv lq Phglflqh/47/ 5744057641

^47` Ehuqduglqhool O1/ Sdvfxwwr F1/ Ehvw Q1J1 h JlonvZ1U1 +4<<:, Glvhdvh pdsslqj

zlwk huuruv lq fryduldwhv/ Vwdwlvwlfv lq Phglflqh/ 49/ :740:851

^48` Ehvdj/ M1 +4<:7, Vsdwldo Lqwhudfwlrq dqg wkh Vwdwlvwlfdo Dqdo|vlv ri Odwwlfh

V|vwhpv +zlwk glvfxvvlrq,1 Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw|/ E/ 69/

4<505691

^49` Ehvdj/ M1 h Juhhq/ S1M1 +4<<6, Vsdwldo Vwdwlvwlfv dqg Ed|hvldq frpsxwdwlrq1

Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw|/ E/ 88/ 5806:1

^4:` Ehvdj/ M1/ Juhhq/ S1M1/ Kljgrq/ G1 h Phqjhuvhq/ N1 +4<<8, Ed|hvldq Frpsx0

wdwlrq dqg Vwrfkdvwlf V|vwhpv1 Vwdwlvwlfdo Vflhqfh/ 43/ 60991

^4;` Ehvdj M1/ \run M1 h Proolì D1+4<<4, Ed|hvldq lpdjh uhvwrudwlrq zlwk wzr ds0

solfdwlrqv lq vsdwldo vwdwlvwlfv/ Dqqdov ri wkh Lqvwlwxwh riVwdwlvwlfv dqg Pdwk0

hpdwlfv/ 76/ 40531

^4<` Ehvdj M1 h Qhzhoo M1 +4<<4, Wkh ghwhfwlrq ri foxvwhuv lq uduh glvhdvhv/ Mrxuqdo

ri Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv D/ 487/ 47604881

Page 124: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

ELEOLRJUDILD 44<

^53` Ehvdj M1 h Nrrshuehuj F1 +4<<8, Rq frqglwlrqdo dqg lqwulqvlf dxwruhjuhvvlrqv/

Elrphwulnd/ ;5/ :660:791

^54` Ehvw Q1/ Lfnvwdgw N1 h Zroshuw U1+4<<;, Vsdwldo Srlvvrq uhjuhvvlrq iru khdowk

dqg h{srvxuh gdwd phdvxuhg dw glvsdudwh vsdwldo vfdohv/ Whfkqlfdo uhsruw/ Gh0

sduwphqw ri Hgslghplrorj| dqg Sxeolf Khdowk/ Lpshuldo Froohjh Vfkrro ri

Phglflqh/ Vw Pdu|*v/ Orqgrq1

^55` Eljjhul D1/ Eduerqh I1/ Odjd}lr F1/ Eryhq}l P1 h Vwdqwd J1 +4<<9, Dlu sro0

oxwlrq dqg oxqj fdqfhu lq Wulhvwh= vsdwldo dqdo|vlv ri ulvn dv d ixqfwlrq ri

glvwdqfh iurp vrxufhv/ Hqylurqphqwdo Khdowk Shuvshfwlyhv/ 437/ :830:871

^56` Elwkhoo M1 +4<<3, Dq dssolfdwlrq ri ghqvlw| hvwlpdwlrq wr jhrjudklfdo hslghpl0

rorj|/ Vwdwlvwlfv lq Phglflqh/ </ 9<40:341

^57` Elwkhoo M1 +4<<8, Wkh fkrlfh ri whvw iru ghwhfwlqj udlvhg glvhdvh ulvn qhdu d

srlqw vrxufh/ Vwdwlvwlfv lq Phglflqh/ 47/ 563<056551

^58` Euloolqjhu/ G1 +4<;9, Wkh qdwxudo yduldelolw| ri ylwdo udwhv dqg dvvrfldwhg

vwdwlvwlfv/ Elrphwulfv/ 75/ 9<60:671

^59` Eurrnv V1 +4<<;, Pdunry Fkdlq Prqwh Fduor dqg lwv dssolfdwlrq/ Mrxuqdo ri

Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv G/ 7:/ 9<04331

^5:` Euxqvgrq F1/ Irwkhulqjkdp V1 dqg Fkduowrq P1/ +4<<;, Jhrjudsklfdoo|

zhljkwhg uhjuhvvlrq�prghoolqj vsdwldo qrq0vwdwlrqdulw|/ Mrxuqdo ri Ur|do Vwd0

wlvwlfdo Vrflhw|/ Vhulhv G/ 7:/ 76407771

^5;` Fduudw I1 dqg Ydoohurq D1 +4<<5, Hslghplrorjlfdo pdsslqj xvlqj wkh cnuljlqj*

phwkrg= dssolfdwlrq wr dq lq xhq}d0olnh looqhvv hslghplf lq Iudqfh/ Dphulfdq

Mrxuqdo ri Hslghplrorj|/ 468/ 45<6046331

^5<` Fkr|qrzvnl/ P1 +4<8<, Pdsv edvhg rq suredelolwlhv1 Mrxuqdo ri wkh Dphulfdq

Vwdwlvwlfdo Dvvrfldwlrq/ 87/ 6;806;;1

^63` Fkulvwdnrv J1 dqg Ol [1\1 +4<<;, Ed|hvldq pd{lpxp hqwurs| dqdo|vlv dqg

pdsslqj= D iduhzhoo wr nuljlqj hvwlpdwruvB Pdwkhpdwlfdo Jhrorj|/ 63/ 7680

7951

Page 125: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

453 ELEOLRJUDILD

^64` Fkulvwldqvhq F1 dqg Pruulv F1 +4<<:, Klhudufklfdo Srlvvrq uhjuhvvlrq prg0

hoolqj/ Mrxuqdo ri Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ <5/ 94;09651

^65` Flvodjkl F1/ Eljjhul D1/ Eudjd P1/ Odjd}lr F1 dqg Pdufkl P1 +4<<8, H{0

sorudwru| wrrov iru glvhdvh pdsslqj lq jhrjudsklf hslghplrorj|/ Vwdwlvwlfv lq

Phglflqh/ 47/ 5696056;41

^66` Fod|wrq G1 h Ndogru M1/ +4<;:, Hpslulfdo Ed|hv hvwlpdwhv ri djh0vwdqgduglvhg

uhodwlyh ulvnv iru xvh lq glvhdvh pdsslqj/ Elrphwulfv/ 76/ 9:409;41

^67` Fod|wrq G1/ Ehuqduglqhool O1 h Prqwrprol F1 +4<<6, Vsdwldo fruuhodwlrq dqg

hfrorjlfdo dqdo|vlv/ Lqwhuqdwlrqdo Mrxuqdo ri Hslghplrorj|/ 55/ 44<6045341

^68` Fod|wrq G1 h Ehuqduglqhool O1 +4<<9, Ed|hvldq phwkrgv iru pdsslqj glvhdvh

ulvn/ lq Hoolrw S1/ Fx}lfn M1/ Hqjolvk G1/ Vwhuq U1 +hgv1, Jhrjudsklf dqg Hqyl0

urqphqwdo Hslghplrorj|= Phwkrgv iru vpdoo duhd vwxglhv/ R{irug Xqlyhuvlw|

Suhvv/ 53805531

^69` Fol�/ D1G1 h Rug/ M1 N1 +4<;4, Vsdwldo Surfhvvhv/ Slrq/ Orqgrq1

^6:` Frohv V1J1 h Srzhoo H1D1+4<<9, Ed|hvldq phwkrgv lq h{wuhph ydoxh prghoolqj=

D uhylhz dqg qhz ghyhorsphqwv/ Lqwhuqdwlrqdo Vwdwlvwlfdo Uhylhz/ 97/ 44<04691

^6;` Frqjgrq S1 +4<<;, D pxowlohyho prgho iru lqidqw khdowk rxwfrphv= pdwhuqdo

ulvn idfwruv dqg jhrjudsklf yduldwlrq/ Mrxuqdo ri Ur|do Vwdwlvwlfdo Vrflhw|/

Vhulhv G/ 7:/ 48<04;51

^6<` Fuhvvlh/ Q1 +4<<5, Vprrwklqj uhjlrqdo pdsv xvlqj hpslulfdo Ed|hv suuhglfwruv1

Jhrjudsklfdo Dqdo|vlv/ 57/ :80<:1

^73` Fuhvvlh Q1 +4<<6, Vwdwlvwlfv iru Vsdwldo Gdwd/ Zloh|1

^74` Fuhvvlh Q1 +4<<9, Ed|hvldq dqg frqvwudlqhg lqihuhqfh iru h{wuhphv lq hsl0

ghplrorj|/ Hslghplrorj| Surfhhglqjv ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/

Mrlqw Phhwlqjv 4<<8/ DVD/ Doh{dqguld/ 4404:1

^75` Fuhvvlh Q1 dqg Gdylgvrq M1O1 +4<<;, Lpdjh dqdo|vlv zlwk sduwldoo| rughuhg

pdunry prghov/ Frpsxwdwlrqdo Vwdwlvwlfv dqg Gdwd Dqdo|vlv/ 5</ 40591

^76` Fx}lfn M1 dqg Hgzdugv U1 +4<<3, Vsdwldo foxvwhulqj iru lqkrprjhqhrxv srs0

xodwlrqv/ Mrxuqdo ri Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv E/ 85/ :604371

Page 126: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

ELEOLRJUDILD 454

^77` Gdwfx P1/ Vhlgho N1 dqg Zdohvvd P1 +4<<;, Vsdwldo lqirupdwlrq uhwulhydo iurp

uhprwh0vhqvlqj lpdjhv 0 Sduw 4= Lqirupdwlrq wkhruhwlfdo shuvshfwlyh/ LHHH

Wudqvdfwlrqv rq Jhrvflhqfh dqg Uhprwh Vhqvlqj/ 69/ 4764047781

^78` Ghylqh R1 dqg Orxlv W1 +4<<7, D frqvwudlqhg hpslulfdo Ed|hv hvwlpdwru iru

lqflghqfh udwhv lq duhdv zlwk vpdoo srsxodwlrqv/ Vwdwlvwlfv lq Phglflqh/ 46/

444<044661

^79` Ghylqh/ R1/ Orxlv/ W1 D1/ Kdoorudq/ P1 H1 +4<<7, Hpslulfdo Ed|hv phwkrgv

iru vwdelol}lqj lqflghqfh udwhv sulru wr pdsslqj1 Hslghplrorj| BBB

^7:` Gljjoh S1 dqg Fkhwz|qg D1 +4<<4, Vhfrqg0rughu dqdo|vlv ri vsdwldo foxvwhulqj

iru lqkrprjhqhrxv srsxodwlrqv/ Elrphwulfv/ 7:/ 4488044961

^7;` Gljjoh S1M1 dqg Ulfkdugvrq V1 +4<<6, Hslghplorjlf Vwxglhv ri Lqgxvwuldo Sro0

oxwdqwv 0 Dq Lqwurgxfwlrq/ Lqwhuqdwlrqdo Vwdwlvwlfdo Uhylhz/ 94/ 53605391

^7<` Gljjoh S1/ Oldqj N0\1 dqg ]hjhu V1O1 +4<<7d, Dqdo|vlv ri Orqjlwxglqdo Gdwd/

Foduhqgrq Suhvv1

^83` Gljjoh S1 dqg Urzolqjvrq E1V1+4<<7e, D Frqglwlrqdo Dssurdfk wr Srlqw Sur0

fhvv Prghoolqj ri Hohydwhg Ulvn/ Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv

D/ 48:/ 76607731

^84` Gljjoh S1 dqg Hoolrww S1 +4<<8, Glvhdvh ulvn qhdu srlqw vrxufhv= Vwdwlvwlfdo

lvvxhv iru dqdo|vhv xvlqj lqglylgxdo ru vsdwldoo| djjuhjdwhg gdwd/ Mrxuqdo ri

Hslgholrorj| dqg Frppxqlw| Khdowk/ 7</ V530V5:1

^85` Gljjoh S1M1/ Pruulv V1/ Hoolrww S1 dqg Vkdgglfn J1 +4<<:, Uhjuhvvlrq prghoolqj

ri glvhdvh ulvn lq uhodwlrq wr srlqw vrxufhv/ Mrxuqdo ri Ur|do Vwdwlvwlfdo Vrflhw|/

Vhulhv D/ 493/ 7<408381

^86` Gljjoh S1M1 h Ulehlur Mu1/ S1 M1 +5333, Prgho0edvhg jhrvwdwlvwlfv1 Dvvrfldêæ

Eudvlohlud gh Hvwdw�vwlfd/ Fd{dpex1

^87` Gljjoh S1M1/ Wdzq M1D1 dqg Pr|hhg U1D1 +4<<;, Prgho0edvhg jhrvwdwlvwlfv/

Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv F/ 7:/ 5<<06591

^88` Hoolrw S1/ Fx}lfn M1/ Hqjolvk G1/ Vwhuq U1 +hgv1, +4<<9, Jhrjudsklf dqg Hqyl0

urqphqwdo Hslghplrorj|= Phwkrgv iru vpdoo duhd vwxglhv/ R{irug Xqlyhuvlw|

Suhvv1

Page 127: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

455 ELEOLRJUDILD

^89` Jdugqhu/ P1 M1 +4<;<, Uhylhz ri uhsruwhg lqfuhdvhv ri fklogkrrg fdqfhu udwhv

lq wkh ylflqlw| ri qxfohdu lqvwdoodwlrqv lq wkh XN1 Mrxuqdo ri wkh Ur|do Vwdwlv0

wlfdo Vrflhw|/ Vìulh D/ 485/ 63:06581

^8:` Jdwuhoo D/ Or|wrqhq P1 +hgv1, +4<<;, JLV dqg Khdowk lq Hxursh/ Wd|oru dqg

Iudqflv1

^8;` Jdxgdug P1/ Nduvrq P1/ Olqghu H1 dqg Vlqkd G1 +4<<<, Ed|hvldq vsdwldo

suhglfwlrq/ Hqylurqphqwdo dqg Hfrorjlfdo Vwdwlvwlfv/ 9/ 47:04:41

^8<` Jhdu|/ U1 F1 +4<87, Wkh frqwljxlw| udwlr dqg vwdwlvwlfdo pdsslqj1 Wkh Lqfru0

srudwhg Vwdwlvwlfldq/ 8/ 44804781

^93` Jhoidqg/ D1 H1/ Jkrvk/ V1 N1/ Nqljkw/ M1 U1 dqg Vlupdqv/ F1I1 +4<<8, Vsdwlr0

Whpsrudo Prgholqj ri Uhvlghqwldo Vdohv Gdwd1 xqsxeolvkhg pdqxvfulsw1

^94` Jhwlv D1 +4<<5, Vsdwldo lqwhudfwlrq dqg vsdwldo dxwrfruuhodwlrq= d furvv surg0

xfw dssurdfk/ Hqylurqphqw dqg Sodqqlqj D/ 56/ 459<045::1

^95` Jkrvk/ P1 +4<<5, Frqvwudlqhg Ed|hv hvwlpdwlrq zlwk dssolfdwlrqv1 Mrxuqdo

ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ ;:/ 86608731

^96` Jkrvk P1/ Qdwdudmdq N1/ Vwurxg W1Z1I/ dqg Fduolq E1S1 +4<<;, Jhqhudol}hg

olqhdu prghov iru vpdoo0duhd hvwlpdwlrq/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo

Dvvrfldwlrq/ <6/ 774/ 5:605;5

^97` Jlonv Z1/ Fod|wrq G1/ Vslhjhokdowhu G1/ Ehvw Q1/ PfQhlo D1/ Vkdsohv O1 dqg

Nlue| D1 +4<<6, Prghoolqj frpsoh{lw|= dssolfdwlrqv ri Jleev vdpsolqj lq

phglflqh/ Mrxuqdo ri Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv E/ 88/ 6<04351

^98` Jlonv Z1U1/ Ulfkdugvrq V1 dqg Vslhjhokdowhu G1 +hgv1, +4<<9, Pdunry Fkdlq

Prqwh Fduor lq Sudfwlfh/ Fkdspdq dqg Kdoo1

^99` Jodvv/ J1 H1/ Vfkzduw}/ E1 V1/ Prujdq/ M1 P1/ Mrkqvrq/ G1 W1/ Qr|/ S1 P1/

Lvudho/ H1 +4<<8, Hqylurqphqwdo ulvn idfwruv iru O|ph glvhdvh lghqwl�hg zlwk

jhrjudsklf lqirupdwlrq v|vwhpv1 Dphulfdq Mrxuqdo ri Sxeolf Khdowk/ ;8/ <770

<7;1

^9:` Jrogvwhlq K1 +4<<8, Pxowlohyho Vwdwlvwlfdo Prghov/ Hgzdug Duqrog1

Page 128: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

ELEOLRJUDILD 456

^9;` Juhhq S1 dqg Vloyhupdq E1 +4<<7, Qrq Sdudphwulf Uhjuhvvlrq dqg Jhqhudolvhg

Olqhdu Prghov/ Fkdspdq dqg Kdoo1

^9<` Kdlqlqj U1/ Zlvh V1 dqg Pd M1V1 +4<<;, H{sorudwru| vsdwldo gdwd dqdo|vlv lq d

jhrjudsklf lqirupdwlrq v|vwhp hqylurqphqw/ Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo

Vrflhw|/ Vhulhv G/ 7:/ 78:079<1

^:3` Kdvwlh W1 dqg Wlevkludql U1 +4<<3, Jhqhudolvhg Dgglwlyh Prghov/ Fkdspdq

dqg Kdoo1

^:4` Kdoorudq H1 dqg Juhhqkrxvh M1 +hgv1, +4<<:, Vwdwlvwlfv dqg Hslghplrorj|=

Hqylurqphqw dqg Khdowk/ Vsulqjhu0Yhodj1

^:5` Kloov P1 dqg Doh{dqghu I1 +4<;<, Vwdwlvwlfdo phwkrgv xvhg lq dvvhvvlqj wkh

ulvn ri glvhdvh qhdu d vrxufh ri srvvleoh hqylurqphqwdo srooxwlrq= d uhylhz/

Mrxuqdo ri Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv D/ 485/ 68606961

^:6` Krryhu/ U1 Q1/ Vwudvvhu/ S1 K1 +4<;3, Duwl�fldo vzhhwhqhuv dqg kxpdq eodgghu

fdqfhu= suholplqdu| uhvxowv1 Odqfhw/ 4/ ;6:0;731

^:7` Mdftxh} J1P1 +4<<9d, D n0qhduhvw qhljkerxu whvw iru vsdfh0wlph lqwhudfwlrq/

Vwdwlvwlfv lq Phglflqh/ 48/ 4<6804<7<1

^:8` Mdftxh} J1P1 +4<<9e, Glvhdvh Foxvwhu vwdwlvwlfv iru lpsuhflvh vsdfh0wlph or0

fdwlrqv/ Vwdwlvwlfv lq Phglflqh/ 48/ ;:60;;81

^:9` Nhovdoo M1H1 h Gljjoh S1M1 +4<<8, QrqSdudphwulf hvwlpdwlrq ri vsdwldo yduldwlrq

lq uhodwlyh ulvn/ Vwdwlvwlfv lq Phglflqh/ 47/ 5668056751

^::` Nhovdoo M1H1 dqg Gljjoh S1M1 +4<<;, Vsdwldo yduldwlrq lq ulvn ri glvhdvh= d

qrqsdudphwulf elqdu| uhjuhvvlrq dssurdfk/ Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo

Vrflhw|/ Vhulhv F/ 7:/ 88<08:61

^:;` Nqruu0Khog O1 dqg Ehvdj M1 +4<<;, Prghoolqj ulvn iurp d glvhdvh lq wlph dqg

vsdfh/ Vwdwlvwlfv lq Phglflqh/ 4:/ 5378053931

^:<` Nqr{ H1J1 +4<97, Wkh ghwhfwlrq ri vsdfh0wlph lqwhudfwlrqv/ Dssolhg Vwdwlvwlfv/

46/ 5805<1

Page 129: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

457 ELEOLRJUDILD

^;3` Nqr{/ H1 J1 +4<;<, Ghwhfwlrq ri Foxvwhuv1 Hp Phwkrgrorj| ri hqtxlulhv lqwr

glvhdvh foxvwhulqj/ S1 Hoolrww +hglwru,1 Orqgrq= Vpdoo Duhd Khdowk Vwdwlvwlfv

Xqlw1

^;4` Nrulh V1/ Fodun V1M1/ Shuu| M1Q1/ Pxjjohvwrqh P1D1/ Eduwohww S1Z1/ Pduvkdoo

H1M1S1 dqg Pdqq M1D1 +4<<;, Dqdo|}lqj pdsv ri glvshuvdo durxqg d vlqjoh

irfxv/ Hqylurqphqwdo dqg Hfrorjlfdo Vwdwlvwlfv/ 8/ 64:06771

^;5` Nxoogrui P1 dqg Qdjduzdood Q1 +4<<8, Vsdwldo glvhdvh foxvwhuv= ghwhfwlrq dqg

lqihuhqfh/ Vwdwlvwlfv lq Phglflqh/ 47/ :<<0;43

^;6` Nxoogrui P1 +4<<:, D vsdwldo vfdq vwdwlvwlf/ Frppxqlfdwlrqv lq Vwdwlvwlfv 0

Wkhru| dqg Phwkrgv/ 59/ 47;4047<91

^;7` Nxoogrui P1/ Ihxhu H1M1/ Ploohu E1D1 dqg Iuhhgpdq O1V1 +4<<:, Euhdvw fdqfhu

foxvwhuv lq wkh qruwkhdvw Xqlwhg Vwdwhv= D jhrjudsklf dqdo|vlv/ Dphulfdq

Mrxuqdo ri Hslghplrorj|/ 479/ 49404:31

^;8` Nxoogrui P1 dqg Kmdopduv X1+4<<<, Wkh Nqr{ phwkrg dqg rwkhu whvwv iru

vsdfh0wlph lqwhudfwlrq/ Elrphwulfv/ 88/ 87708851

^;9` N|uldnlglv S1F1 dqg Mrxuqho D1J1 +4<<<, Jhrvwdwlvwlfdo vsdfh0wlph prghov= D

uhylhz/ Pdwkhpdwlfdo Jhrorj|/ 64/ 98409;71

^;:` Odqjirug L1 dqg Ohzlv W1 +4<<;, Rxwolhuv lq pxowl0ohyho prghov/ Mrxuqdo ri

Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv D/ 434/ 45404931

^;;` Odzvrq D1 +4<<6, Rq wkh dqdo|vlv ri pruwdolw| hyhqwv durxqg d suhvshfl�hg

�{hg srlqw/ Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv D/ 489/ 69606::1

^;<` Odzvrq D1 +4<<8, Pdunry Fkdlq Prqwh Fduor phwkrgv iru sxwdwlyh sroxwlrq

vrxufh sureohpv lq hqylurqphqwdo hslghplrorj|/ Vwdwlvwlfv lq Phglflqh/ 47/

57:6057;91

^<3` Odzvrq D1 dqg Ylho M1 +4<<8, Whvwv iru gluhfwlrqdo vsdfh0wlph lqwhudfwlrq lq

hslghplrorjlfdo vwxglhv/ Vwdwlvwlfv lq Phglflqh/ 47/ 56;6056<51

^<4` Odzvrq D1 dqg Zdoohu O1 +4<<9, D uhylhz ri srlqw sdwwhuq phwkrgv iru vsdwldo

prghoolqj ri hyhqwv durxqg vrxufhv ri srooxwlrq/ Hqylurqphwulfv/ :/ 7:407;;1

Page 130: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

ELEOLRJUDILD 458

^<5` Odzvrq D1/ Eljjhul D1/ Eùkqlqj G1/ Ohvd�uh H1/ Ylho M0I1 dqg Ehuwroolql U1

+hgv1, +4<<<d, Glvhdvh Pdsslqj dqg Ulvn Dvvhvvphqw iru Sxeolf Khdowk/ Zloh|1

^<6` Odzvrq D1/ Eljjhul D1 dqg Guhdvvd H1 +4<<<e, Hgjh h�hfwv lq glvhdvh pdsslqj/

lq Odzvrq D1/ Eljjhul D1/ Eùkqlqj G1/ Ohvd�uh H1/ Ylho M0I1 dqg Ehuwroolql U1

+hgv1, Glvhdvh Pdsslqj dqg Ulvn Dvvhvvphqw iru Sxeolf Khdowk/ Zloh|/ ;80<:1

^<7` Odzvrq D1 dqg Fodun D1 +4<<<, Pdunry Fkdlq Prqwh Fduor phwkrgv iru

foxvwhulqj lq fdvh hyhqw dqg frxqw gdwd lq vsdwldo hslghplrorj|/ lq Kdoorudq

H1 dqg Juhhqkrxvh M1 +hgv1, Vwdwlvwlfv dqg Hslghplrorj|= Hqylurqphqw dqg

Khdowk/ Vsulqjhu0Yhodj1

^<8` Pdqwho Q1 +4<9:, Wkh ghwhfwlrq ri glvhdvh foxvwhulqj dqg d jhqhudolvhg uhjuhv0

vlrq dssurdfk/ Fdqfhu Uhvhdufk/ 5:/ 53<05531

^<9` Pdqwrq/ N1 J1/ Zrrgexu|/ P1 D1/ Vwdoodug/ H1/ Uljjdq/ Z1 E1/ Fuhdvrq/ M1

S1/ Shoorp/ D1 F1 +4<;<, Hpslulfdo Ed|hv Surfhgxuhv iru Vwdelol}lqj Pdsv ri

X1V1 Fdqfhu Pruwdolw| Udwhv1 Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/

;7/ 96:09831

^<:` Pduvkdoo/ U1 +4<<4, Pdsslqj glvhdvh dqg pruwdolw| udwhv xvlqj hpslulfdo

Ed|hv hvwlpdwruv1 Dssolhg Vwdwlvwlfv/ 73/ 5;605<71

^<;` Pdvrq/ W1 M1 +4<<8, Wkh ghyhorsphqw ri wkh vhulhv ri X1V1 fdqfhu dwodvhv=

lpsolfdwlrqv iru wkh ixwxuh hslghplorjlf uhvhdufk1 Vwdwlvwlfv lq Phglflqh/ 47/

7:607:<1

^<<` Pdvrq/ W1 M1/ PfNd|/ I1 Z1/ Krryhu/ U1/ Eorw/ Z1M1/ dqg Iudxphql/ M1 I1

+4<:8, Dwodv ri Fdqfhu Pruwdolw| iru X1V1 Frxqwlhv/ 4<8304<9<1 Ghsduwphqw

ri Khdowk/ Hgxfdwlrq/ dqg Zhoiduh Sxeolfdwlrq :80:;3/ Zdvklqjwrq/ GF= XV

Jryhuqphqw Sulqwlqj R!fh1

^433` Pdvrq/ W1 M1/ PfNd|/ I1 Z1/ Krryhu/ U1/ Eorw/ Z1M1/ dqg Iudxphql/ M1 I1

+4<:8, Dwodv ri Fdqfhu Pruwdolw| dprqj X1V1 Qrqzklwhv= 4<8304<9<1 Ghsduw0

phqw ri Khdowk/ Hgxfdwlrq/ dqg Zhoiduh Sxeolfdwlrq :904537/ Zdvklqjwrq/

GF= XV Jryhuqphqw Sulqwlqj R!fh1

^434` Pduwx}}l P1 dqg Hoolrww S1 +4<<9, Hpslulfdo Ed|hv hvwlpdwlrq ri vpdoo duhd

suhydohqfh lq qrq0uduh frqglwlrqv/ Vwdwlvwlfv lq Phglflqh/ 48/ 4;9:0:61

Page 131: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

459 ELEOLRJUDILD

^435` Proolì/ D1 Ulfkdugvrq/ V1 +4<<4, Hpslulfdo Ed|hv hvwlpdwhv ri fdqfhu pru0

wdolw| udwhv xvlqj vsdwldo prghov1 Vwdwlvwlfv lq Phglflqh/ 43/ <804451

^436` Proolì D1 +4<<8, Ed|hvldq pdsslqj ri glvhdvh/ lq Jlonv Z1U1/ Ulfkdugvrq V1

dqg Vslhjhokdowhu G1M1 +hgv1, Pdunry Fkdlq Prqwh Fduor lq Sudfwlfh/ Fkds0

pdq ) Kdoo/ 68<06:<1

^437` Prudq/ S1 D1 S1 +4<87, Wkh lqwhusuhwdwlrq ri vwdwlvwlfdo pdsv1 Mrxuqdo ri

Ur|do Vwdwlvwlfdo Vrflhw|/ vhulhv E/ 43/ 57605841

^438` Pxoohu K1J1/ Vwdgwpxoohu X1 dqg Wdeqdn I1 +4<<:, Vsdwldo vprrwklqj ri jhr0

judsklfdoo| djjuhjdwhg gdwd/ zlwk dssolfdwlrq wr wkh frqvwuxfwlrq ri lqflghqfh

pdsv/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ <5/ 76:/ 940:41

^439` Qhxwud U1U1 +4<<3, Frxqwhusrlqw iurp d foxvwhu exvwhu/ Dphulfdq Mrxuqdo

ri Hslghplrorj|/ 465/ Vxssohphqw/ 40;1

^43:` Qhxwud U1U1 +4<<<, Frpsxwhu jhrjudsklf dqdo|vlv= d frpphqwud| rq lwv xvh

dqg plvxvh lq sxeolf khdowk/ lq Odzvrq D1/ Eljjhul D1/ Eùkqlqj G1/ Ohvd�uh

H1/ Ylho M0I1 dqg Ehuwroolql U1 +hgv1, Glvhdvh Pdsslqj dqg Ulvn Dvvhvvphqw

iru Sxeolf Khdowk/ Zloh|/ 644064<1

^43;` Rghq Q1 +4<<8, Dgmxvwlqj Prudq*v L iru srsxodwlrq ghqvlw|/ Vwdwlvwlfv lq

Phglflqh/ 47/ 4:0591

^43<` Rovhq V1/ Pduwx}}l P1 dqg Hoolrww S1 +4<<9, Foxvwhu dqdo|vlv dqg glvhdvh

pdsslqj0zk|/ zkhq/ krzB D vwhs e| vwhs jxlgh/ Eulwlvk Phglfdo Mrxuqdo/

646/ ;960;981

^443` Rshqvkdz/ V1/ Fudiw/ D1 Z1/ Fkduowrq/ P1 J1/ h Elufk/ M1 P1 +4<;;, Lqyhvwl0

jdwlrq ri ohxndhpld foxvwhuv e| xvh ri d jhrjudsklfdo dqdo|vlv pdfklqh1 Odqfhw/

5:505:61

^444` Rshqvkdz V1 +4<<4, D qhz dssurdfk wr wkh ghwhfwlrq dqg ydolgdwlrq ri

fdqfhu foxvwhuv= d uhylhz ri rssruwxqlwlhv/ surjuhvv dqg sureohpv/ lq Gxqvwdq

I1/ Slfnohv M1 +hgv1, Vwdwlvwlfv lq Phglflqh/ 43/ 7<0961

^445` Slfnoh/ O1 Z1/ Juhhqh/ P1 K1/ ]lhjohu/ U1 J1/ Wrohgr/ D1/ Krryhu/ U1/ O|qfk/

K1 W1/ Iudxphql/ M1 I1/ Mu1 +4<;4, Froruhfwdo fdqfhu lq uxudo Qheudvnd1 Fdqfhu

Uhvhdufk/ 77/ 696069<1

Page 132: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

ELEOLRJUDILD 45:

^446` Slhjruvfk Z1Z1/ Vplwk H1S1/ Hgzdugv G1 dqg Vplwk U1O1 +4<<;, Vwdwlvwlfdo

dgydqfhv lq hqylurqphqwdo vflhqfh/ Vwdwlvwlfdo Vflhqfh/ 46/ 4;9053;1

^447` Soxpphu P1 dqg Fod|wrq G1 +4<<9, Hvwlpdwlrq ri srsxodwlrq h{srvxuh lq

hfrorjlfdo vwxglhv/ Mrxuqdo ri Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv E/ 8;/ 44604591

^448` Srwwkr� U1I1 dqgZklwwlqjkloo P1 +4<99, Whvwlqj iru Krprjhqhlw|/ Elrphwul0

nd/ 86/ 49:04<31

^449` Suhqwlfh U1 dqg Vkhssdug O1 Djjuhjdwh gdwd vwxglhv ri glvhdvh ulvn idfwruv/

Elrphwulnd/ ;5/ 44604581

^44:` Ulfkdugvrq V1/ Jxlkhqqhxf F1 dqg Odvvhuuh Y1 +4<<5, Vsdwldo olqhdu prghov

zlwk dxwrfruuhodwhg huuru vwuxfwxuh/ Mrxuqdo ri Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv

G/ 74/ 86<088:1

^44;` Ulfkdugvrq V1 dqg Juhhq S1 +4<<:, Rq Ed|hvldq dqdo|vlv ri pl{wxuhv zlwk dq

xqnqrzq qxpehu ri frpsrqhqwv/ Mrxuqdo ri Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv

E/ 8</ :640:<51

^44<` Ulsoh|/ E1 G1 +4<::, Prghoolqj vsdwldo sdwwhuqv +zlwk glvfxvvlrq,1 Mrxuqdo

ri Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv E/ 6</ 4:505451

^453` Uxvkwrq J1/ Nulvkqdpxuwk| U1/ Nulvkqdpxuwl G1/ Ororqlv S1 dqg Vrqj K1

+4<<9, Wkh vsdwldo uhodwlrqvkls ehwzhhq lqidqw pruwdolw| dqg eluwk ghihfw udwhv

lq d XV flw|/ Vwdwlvwlfv lq Phglflqh/ 48/ 4<3:04<4<1

^454` Vfkdowwpdqq S1 dqg Eùkqlqj G1 +4<<6, Pl{wxuh prghov dqg glvhdvh pdsslqj/

Vwdwlvwlfv lq Phglflqh/ 45/ 4<7604<831

^455` Vfkdowwpdqq S1/ Eùkqlqj G1 dqg Glhw} H1 +4<<9, Fryduldwh dgmxvwhg pl{wxuh

prghov zlwk wkh surjudp GlvpdsZlq/ Vwdwlvwlfv lq Phglflqh/ 48/ <4<0<5<1

^456` Vfkurghu P1/ Uhkudxhu K1/ Vhlgho N1 dqg Gdwfx P1 +4<<;, Vsdwldo lqirupd0

wlrq uhwulhydo iurp uhprwh0vhqvlqj lpdjhv 0 Sduw LL= Jleev0Pdunry udqgrp

�hogv/ LHHH Wudqvdwlrqv rq Jhrvflhqfh dqg Uhprwh Vhqvlqj/ 69/ 4779047881

^457` Vslhjhokdowhu G1/ Wkrpdv D1/ Ehvw Q1 dqg Jlonv Z1 +4<<:, EXJV= Ed|hvldq

Lqihuhqfh xvlqj Jleev Vdpsolqj/ PUF Elrvwdwlvwlfv Xqlw/ Fdpeulgjh/ XN1

Page 133: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

45; ELEOLRJUDILD

^458` Vslhjhokdowhu G1 +4<<;, Ed|hvldq judsklfdo prghoolqj= d fdvh vwxg| lq prq0

lwrulqj khdowk rxwfrphv/ Mrxuqdo ri Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv F/ 7:/

44804661

^459` Vwhlq D1/ YdqJurhqljhq M1Z1/ Mhjhu P1M1 dqg Krrvehhn P1U1 +4<<;d, Vsdfh0

wlph vwdwlvwlfv iru hqylurqphqwdo dqg djulfxowxudo uhodwhg skhqrphqd/ Hqyl0

urqphqwdo dqg Hfrorjlfdo Vwdwlvwlfv/ 8/ 48804:51

^45:` Vwhlq D1/ Edvwlddqvvhq Z1J1P1/ GhEuxlq V1/ Fudfnqhoo D1S1/ Fxuudq S1M1/

Ideeul D1J1/ Jruwh E1J1K1/ YdqJurhqljhq M1Z1/ YdqghuPhhu I1G1 dqg Vdo0

gdqd D1 +4<<;e, Lqwhjudwlqj vsdwldo vwdwlvwlfv dqg uhprwh vhqvlqj/ Lqwhuqd0

wlrqdo Mrxuqdo ri Uhprwh Vhqvlqj/ 4</ 4:<604;471

^45;` Vwrqh U1 +4<;;, Lqyhvwljdwlrqv ri h{fhvv hqylurqphqwdo ulvnv durxqg sxwdwlyh

vrxufhv= vwdwlvwlfdo sureohpv dqg d sursrvhg whvw/ Vwdwlvwlfv lq Phglflqh/ :/

97<09931

^45<` Wdqjr W1 +4<<8, D fodvv ri whvw iru ghwhfwlqj cjhqhudo* dqg *irfxvhg* foxvwhulqj

ri uduh glvhdvhv/ Vwdwlvwlfv lq Phglflqh/ 47/ 5656056671

^463` Wkrpvrq P1F1/ Frqqru V1M1/ Gdohvvdqgur X1/ Urzolqjvrq E1/ Gljjoh S1/

Fuhvvzhoo P1 dqg Juhhqzrrg E1 +4<<<, Suhglfwlqj pdoduld lqihfwlrq lq Jdp0

eldq fkloguhq iurp vdwhoolwh gdwd dqg ehg qhw xvh vxuyh|v= Wkh lpsruwdqfh

ri vsdwldo fruuhodwlrq lq wkh lqwhusuhwdwlrq ri uhvxowv/ Dphulfdq Mrxuqdo ri

Wurslfdo Phglflqh dqg K|jlhqh/ 94/ 50;1

^464` Wmhophodqg K1 dqg Ehvdj M1 +4<<;, Pdunry udqgrp �hogv zlwk kljkhu0rughu

lqwhudfwlrqv/ Vfdqglqdyldq Mrxuqdo ri Vwdwlvwlfv/ 58/ 74807661

^465` Wroqd|/ V1 H1 h Ghdqh/ J1 +4<<9, Ylfdulrxv ylrohqfh= vsdwldo h�hfwv rq Vrxwk0

huq o|qfklqjv/ 4;<304<4<1 Dphulfdq Mrxuqdo ri Vrflrorj|/ 435/ :;;0;481

^466` Wvxwdndzd/ U1N1 +4<;;, Pl{hg Prgho iru Dqdo|vlqj Jhrjudsklf Yduldwlrq lq

Pruwdolw| Udwhv1 Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ ;6/ 6:0751

^467` Wvxwdndzd/ U1N1/ Vkrrs/ J1O1/ dqg Pdulhqihog/ F1M1 +4<;8, Hpslulfdo Ed|hv

Hvwlpdwlrq ri Fdqfhu Pruwdolw| Udwhv1 Vwdwlvwlfv lq Phglflqh/ 7/ 53405451

Page 134: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

ELEOLRJUDILD 45<

^468` Wxuqexoo E1/ Lzdqr H1/ Exuqhww Z1/ Krzh K1 dqg Fodun O1 +4<<3, Prqlwrulqj

iru foxvwhuv ri glvhdvh= dssolfdwlrq wr Ohxndhpld lqflghqfh lq xsvwdwh Qhz

\run/ Dphulfdq Mrxuqdo ri Hslghplrorj|/ 465/ 46904761

^469` Xqzlq D1 dqg Xqzlq G1 +4<<;, H{sorudwru| vsdwldo gdwd dqdo|vlv zlwk orfdo

vwdwlvwlfv/ Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv G/ 7:/ 74807541

^46:` Zdogkùu +4<<9, Wkh vsdwldo dxwrfruuhodwlrq frh!flhqw Prudq*v L xqghu khw0

hurvfhgdvwlflw|1 Vwdwlvwlfv lq Phglflqh/ 48/ ;;:0;<51

^46;` Zdoohu O1/ Wxuqexoo E1/ Fodun/ O1 h Qdvfd/ S1 +4<<5, Fkurqlf glvhdvh vxuyhlo0

odqfh dqg whvwlqj ri foxvwhulqj ri glvhdvh dqg h{srvxuh= dssolfdwlrq wr

ohxndhpld lqflghqfh dqg WFH0frqwdplqdwhg gxpsvlwhv lq xsvwdwh Qhz \run1

Hqylurqphwulfv/ 6/ 5;406331

^46<` Zdoohu O1 dqg Wxuqexoo E1 +4<<6, Wkh h�hfw ri vfdoh rq whvwv iru glvhdvh

foxvwhulqj/ Vwdwlvwlfv lq Phglflqh/ 45/ 4;9<04;;71

^473` Zdoohu O1 dqg Odzvrq D1 +4<<8, Wkh srzhu ri irfxvvhg whvwv wr ghwhfw glvhdvh

foxvwhulqj/ Vwdwlvwlfv lq Phglflqh/ 47/ 55<40563;1

^474` Zdoohu O1/ Fduolq E1/ [ld K1 dqg Jhoidqg D1 +4<<:, Klhudufklfdo vsdwlr0

whpsrudo pdsslqj ri glvhdvh udwhv/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvr0

fldwlrq/ <5/ 93:094:1

^475` Zdoohu/ O1 h Srtxhwwh/ F1 +4<<<, Wkh srzhu ri irfxvhg whvwv xqghu plvvshf0

l�hg foxvwhu prghov/ lq Odzvrq D1/ Eljjhul D1/ Eùkqlqj G1/ Ohvd�uh H1/ Ylho

M0I1 dqg Ehuwroolql U1 +hgv1, Glvhdvh Pdsslqj dqg Ulvn Dvvhvvphqw iru Sxeolf

Khdowk/ Zloh|/ 58:059<1

^476` Zdowhu V1 +4<<5, Wkh dqdo|vlv ri uhjlrqdo sdwwhuqv lq khdowk gdwd1 L= Glvwul0

exwlrqdo frqvlghudwlrqv/ Dphulfdq Mrxuqdo ri Hslghplrorj|/ 469/ :630:741

^477` Zdowhu V1 +4<<6d, Ylvxdo dqg vwdwlvwlfdo dvvhvvphqw ri vsdwldo foxvwhulqj lq

pdsshg gdwd/ Vwdwlvwlfv lq Phglflqh/ 45/ 45:8045<41

^478` Zdowhu V1 +4<<6e, Dvvhvvlqj vsdwldo sdwwhuq lq glvhdvh udwhv/ Vwdwlvwlfv lq

Phglflqh/ 45/ 4;;804;<71

Page 135: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

463 ELEOLRJUDILD

^479` Zdowhu V1 +4<<7, D vlpsoh whvw iru vsdwldo sdwwhuq lq uhjlrqdo khdowk gdwd/

Vwdwlvwlfv lq Phglflqh/ 46/ 436:043771

^47:` Zhevwhu U1/ Rolyhu P1/ Pxlu N1 dqg Pdqq M1 +4<<7, Nuljlqj wkh orfdo ulvn ri

d uduh glvhdvh iurp d uhjlvwhu ri gldjqrvhv/ Jhrjudsklfdo Dqdo|vlv/ 59/ 49;04;81

^47;` Zhlu L1V1 dqg Shwwlww D1Q1 +4<<<, Vsdwldo prghoolqj iru elqdu| gdwd xvlqj d

klgghq frqglwlrqdo dxwruhjuhvvlyh Jdxvvldq surfhvv= d pxowlyduldwh h{whqvlrq

ri wkh surelw prgho/ Vwdwlvwlfv dqg Frpsxwlqj/ </ ::0;91

^47<` Zklwwhpruh D1/ Iulhqg Q1/ Eurzq E1 dqg Kroo| H1 +4<;:, D whvw wr ghwhfw

foxvwhuv ri glvhdvh/ Elrphwulnd/ :7/ 96409681

^483` Zlnoh F1N1/ Ehuolqhu O1P1 dqg Fuhvvlh Q1 +4<<;, Klhudufklfdo Ed|hvldq vsdfh0

wlph prghov/ Hqylurqphqwdo dqg Hfrorjlfdo Vwdwlvwlfv/ 8/ 44:04871

^484` Zlokhop D1 dqg Vwhfn U1 +4<<;, H{sorulqj vsdwldo gdwd e| xvlqj lqwhudfwlyh

judsklfv dqg orfdo vwdwlvwlfv/ Mrxuqdo ri wkh Ur|do Vwdwlvwlfdo Vrflhw|/ Vhulhv

G/ 7:/ 75607631

^485` Zlqq/ G1 P1/ Eorw/ Z1 M1/ Vk|/ F1 P1/ Slfnoh/ O1 Z1/ Wrohgr/ D1/ Iudxphql

Mu1/ M1 I1 +4<;4, Vqx� glsslqj dqg rudo fdqfhu dprqj zrphq lq wkh vrxwkhuq

Xqlwhg Vwdwhv1 Qhz Hqjodqg Mrxuqdo ri Phglflqh/ 637/ :780:7<1

^486` Zroshuw U1O1 dqg Lfnvwdgw N1 +4<<;, Srlvvrq2jdppd udqgrp �hog prghov

iru vsdwldo vwdwlvwlfv/ Elrphwulnd/ ;8/ 584059:1

^487` [ld K1/ Fduolq E1S1 dqg Zdoohu O1D1 +4<<:, Klhudufklfdo prghov iru pdsslqj

Rklr oxqj fdqfhu udwhv/ Hqylurqphwulfv/ ;/ 43:04531

^488` [ld/ K1/ dqg Fduolq/ E1 +4<<;, Vsdwlr0whpsrudo prghov zlwk huuruv lq frydul0

dwhv pdsslqj Rklr oxqj fdqfhu pruwdolw|1 Vwdwlvwlfv lq Phglflqh/ 4:/ 53580

53761

^489` \dvxl \1 dqg Ohoh V1 +4<<:, D uhjuhvvlrq phwkrg iru vsdwldo glvhdvh udwhv=

dq hvwlpdwlqj ixqfwlrq dssurdfk/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfl0

dwlrq/ <5/ 540651

^48:` ]lhjohu/ U1 J1/ Pdvrq/ W1 M1/ Vwhpkdjhq/ D1 Krryhu/ U1/ Vfkrhqehuj/ M1 E1/

Ylujr/ S1 Z1/ dowpdq/ U1/ Iudxphql/ m1 I1/ Mu1 +4<;7, Glhwdu| fdurwhqh dqg

Page 136: [Livro] Estatística Espacial com Aplicações em Epidemiologia, Economia e Sociologia

ELEOLRJUDILD 464

ylwdpqlq D dqg ulvn ri oxqj fdqfhu dprqj zklwh phq lq Qhz Mhuvh|1 Mrxuqdo

ri wkh Qdwlrqdo Fdqfhu Lqvwlwxwh/ :6/ 475<047681