All Conditional Distributions for Y Given X that are Compatible with a Given Conditional Distribution for X Given Y

Abstract

For a given conditional distribution for X given Y, it is important to identify the class of all conditional distributions for Y given X such that there exists at least one bivariate distribution with the given particular conditional densities. Such problems are addressed as dealing with “compatibility” of two conditional distributions. In the present note our goal is to identify all possible conditional densities for Y given X that are compatible with the given family of distributions of X given Y.