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

A new method for constructing absolutely continuous two-dimensional copulas by differential equations is presented. The copulas are symmetric with respect to reflection in the opposite diagonal. The support of the copula density may be prescribed to arbitrary opposite symmetric hypographs of invertible functions, containing the diagonal. The method is applied to toxicological probit modeling, where new compatibility conditions for the probit parameters are derived.