Variations on a Bhattacharyya Theme

Abstract

Bhattacharyya introduced a family of bivariate distributions with normal conditions in 1943. He discussed what additional conditions are required to guarantee that the joint distribution is a classical bivariate normal distribution. The family of distributions with normal conditionals is , in itself, an interesting exponential family. Its structure is discussed in the present paper. Extensions to higher dimensions and to cases in which the conditional distributions are prescribed to belong to non normal families are discussed. These conditionally specified families of distributions are shown to be particularly suitable for use as prior distributions in multiparameter Bayesian Inference settings.