Multivariate Generalized Beta Distributions with Applications to Utility Assessment

Abstract

Two multivariate probability distributions, namely a generalized beta and a generalized F, that appear to be useful in utility modeling are derived. They reduce to the standard beta and F distributions, respectively, in special cases. Reproduction of distributional form is demonstrated for marginal and conditional distributions. Formulas for the moments of these distributions are given. The usefulness of these distributions in utility modeling derives from the fact that they generally do not demand increasing risk aversion as do most standard forms. An example of the use of the bivariate generalized beta distribution in utility modeling is presented. This distribution compares favorably in an example given here to both a normal model and an unstructured model.