Probability of hitting a random vector in a polyhedral cone: Majorization aspect

Abstract

The article presents conditions under which the probability of a linear combination of random vectors falling into a polyhedral cone is a Schur-concave function of the coefficients of the combination. It is required that the cone contains the point 0, its edges are parallel to the coordinate axes, and the distribution density of vectors is a logarithmically concave sign-invariant function.