Computable representations for the general density of random r–contents of beta distributed random points in an n–ball

Abstract

This article considers the r–content of the simplex convex hull of r + 1 independent beta distributed random points in a unit n–ball. By comparing this problem with a similar one in multivariate statistical analysis, the exact density is obtained, for the general case, in computable series form.

AMS 1980 subject classifications:

• Primary 62H10
• secondary 62E05

Keywords:

• Computable representations
• exact densities
• volume of random simplex