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

## TL;DR

This paper introduces a novel differential equations-based method for constructing symmetric absolutely continuous copulas with prescribed support, and applies it to toxicological probit modeling to derive new parameter conditions.

## Contribution

It presents a new mathematical approach for copula construction with customizable support and demonstrates its application in toxicology modeling.

## Key findings

- Copulas can be constructed with arbitrary symmetric support.
- New compatibility conditions for probit model parameters are established.
- The method enhances flexibility in modeling dependencies in toxicology.

## Abstract

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.