A Probability Inequality for Convolutions of MTP2-Distribution Functions

TL;DR

This paper establishes a new probability inequality for convolutions of MTP2 distribution functions, improving upon Gaussian correlation inequalities, with applications to multivariate chi-square distributions from Wishart matrices.

Contribution

It introduces a novel inequality for convolutions of MTP2 distributions, enhancing existing bounds and applicable to multivariate chi-square distributions.

Findings

The inequality outperforms Gaussian correlation inequalities.

Applicable to multivariate chi-square distributions.

Provides new bounds for convolutions of MTP2 functions.

Abstract

A probability inequality is proved for n-fold convolutions of a smooth cumulative distribution function on (0,infinity)x...x(0,infinity), which is multivariate totally positive of order 2 (MTP2). This inequality is better than an inequality of the same type as the Gaussian correlation inequality for distribution functions. An important example are some multivariate chi-square distributions, derived from the diagonal of a Wishart matrix.