Bivariate Distributions with Conditionals in Prescribed Exponential Families

Abstract

SUMMARY We characterize the class of bivariate distributions such that the conditional distributions belong to any specified exponential families. The result leads at once to several bivariate families derived by Castillo and Galambos and by Arnold and Strauss, as well as to distributions with Poisson, geometric and other conditionals. We indicate methods to simulate samples from the distributions and estimate their parameters.