The multivariate Selberg beta distribution and applications

摘要

The classical beta distribution defined on (0,1) is based on Euler's integral of the second type and its generalization to several variables, defined on a simplex, is based on Dirichlet's generalized form of Euler's integral. We define the multivariate Selberg beta random vector X=(X ₁, …, X _p ) MSBeta1 (α, β, γ, p), p≥1, defined on (0, 1) p . This distribution, based on the Selberg integral, a generalized form of the Dirichlet integral, has close relationships with the distributions of roots of determinantal equations and also has several interesting applications, such as the multivariate Gini mean difference.