arXiv:2410.04143 Abstract | arXiv Analytics

arXiv:2410.04143 [math.PR]Abstract References Reviews Resources

A Probability Inequality for Convolutions of MTP2-Distribution Functions

Published 2024-10-05, updated 2025-05-08Version 2

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.

Comments: 4 pages

Categories: math.PR

Subjects: 60E15

Keywords: probability inequality, mtp2-distribution functions, smooth cumulative distribution function, gaussian correlation inequality, multivariate chi-square distributions

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