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A new method for constructing absolutely continuous two--dimensional copulasby differential equations is presented. The copulas are symmetric with respectto reflection in the opposite diagonal. The support of the copula density maybe prescribed to arbitrary opposite symmetric hypographs of invertiblefunctions, containing the diagonal. The method is applied to toxicologicalprobit modeling, where new compatibility conditions for the probit parametersare derived.

Absolutely continuous copulas with prescribed support constructed by differential equations, with an application in toxicology