Computable representations for the general density of random r#x2013;contents of beta distributed random points in an n#x2013;ball

摘要

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.