Constructions for a bivariate beta distribution

TL;DR

This paper introduces a new multivariate beta distribution with flexible correlation structure, positive support, and beta marginals, extending the univariate beta distribution for modeling bivariate probabilities.

Contribution

It proposes a novel multivariate beta distribution with full-range correlations and discusses its extension to higher dimensions, filling a gap in probabilistic modeling.

Findings

Provides a new distribution with beta marginals and full-range correlations.

Ensures positive probability over the entire unit square.

Discusses extension to higher dimensions.

Abstract

The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate beta distribution plays a similar role for two probabilities that have a bivariate binomial distribution. We provide a new multivariate distribution with beta marginal distributions, positive probability over the unit square, and correlations over the full range. We discuss its extension to three or more dimensions.