A Probability Inequality for Convolutions of MTP2-Distribution Functions

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.