A Probability Inequality for Convolutions of MTP2-Distribution Functions

2024/10/05 by Thomas Royen, Royen, Thomas
Computer Science · Mathematics · #60E15 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.2410.04143

openalex publication_date 2024/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Some probability inequalities for multivariate gamma and normal distributions
• Some improved Gaussian correlation inequalities for symmetrical\n n-rectangles extended to some multivariate gamma distributions and some\n further probability inequalities
• An MTP₂ property for conditional distributions
• Total positivity in Markov structures
• Maximum likelihood estimation in Gaussian models under total positivity