Comparison of experiments of some multivariate distributions with a common marginal

Abstract

In this paper we review some current work on comparison of experiments of some multivariate distributions. First we describe some results regarding comparison of experiments of univariate distributions that belong to twoparameters exponential families and that satisfy the semi-group property. Then we discuss comparison of experiments of vectors that arise from an additive model based on univariate two-parameter exponential families of random variables. These models give rise to vectors of random variables which are positively dependent and these are compared to vectors of independent random variables with the same marginals. It is shown that positively dependent random variables contain less information than independent random variables. Finally we describe some results regarding the comparison of experiments of exchangeable and nonexchangeable normal random vectors. In particular, we show how the majorization ordering can be used to identify various information orderings of multivariate normal random vectors which have a common marginal density.