From: Effects of climate on West Nile Virus transmission risk used for public health decision-making in Quebec
Family of copulas
Generator φ (t)
Parameter θ
Bivariate Copula C φ (u, v)
Independent
-ln(t)
uv
Gumbel
(-ln(t))θ
θ ≥ 1
e − [ ( − ln u ) θ + ( − ln v ) θ ] 1 / θ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGLbqzdaahaaWcbeqaaiabgkHiTmaadmaabaGaeiikaGIaeyOeI0IagiiBaWMaeiOBa4MaemyDauNaeiykaKYaaWbaaWqabeaaiiGacqWF4oqCaaWccqGHRaWkcqGGOaakcqGHsislcyGGSbaBcqGGUbGBcqWG2bGDcqGGPaqkdaahaaadbeqaaiab=H7aXbaaaSGaay5waiaaw2faamaaCaaameqabaGaeGymaeJaei4la8Iae8hUdehaaaaaaaa@4734@
Clayton
t-θ-1
θ > 0
(u-θ+ v-θ-1)-1/θ
Frank
− ln ( e − θ t − 1 e − θ − 1 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqGHsislcyGGSbaBcqGGUbGBdaqadaqaamaalaaabaGaemyzau2aaWbaaSqabeaacqGHsisliiGacqWF4oqCcqWG0baDaaGccqGHsislcqaIXaqmaeaacqWGLbqzdaahaaWcbeqaaiabgkHiTiab=H7aXbaakiabgkHiTiabigdaXaaaaiaawIcacaGLPaaaaaa@3F7F@
θ ∈ ℝ
− 1 θ ln ( 1 + ( e − θ u − 1 ) ( e − θ v − 1 ) ( e − θ − 1 ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqGHsisldaWcaaqaaiabigdaXaqaaGGaciab=H7aXbaacyGGSbaBcqGGUbGBdaqadaqaaiabigdaXiabgUcaRmaalaaabaWaaeWaaeaacqWGLbqzdaahaaWcbeqaaiabgkHiTiab=H7aXjabdwha1baakiabgkHiTiabigdaXaGaayjkaiaawMcaamaabmaabaGaemyzau2aaWbaaSqabeaacqGHsislcqWF4oqCcqWG2bGDaaGccqGHsislcqaIXaqmaiaawIcacaGLPaaaaeaadaqadaqaaiabdwgaLnaaCaaaleqabaGaeyOeI0Iae8hUdehaaOGaeyOeI0IaeGymaedacaGLOaGaayzkaaaaaaGaayjkaiaawMcaaaaa@5019@