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Table 5 Archimedean copulas used in this study with their generators

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 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@