Logarithmic complete monotonicity of a matrix-parametrized analogue of the multinomial distribution

TL;DR

This paper introduces a matrix-parametrized generalization of the multinomial distribution, proves its logarithmic complete monotonicity, and derives new inequalities for multivariate gamma functions.

Contribution

It presents a novel matrix-parametrized multinomial analogue and establishes its key monotonicity property along with related inequalities.

Findings

Proves logarithmic complete monotonicity of the new distribution

Derives new inequalities involving ratios of multivariate gamma functions

Introduces a matrix-parametrized generalization of the multinomial distribution

Abstract

In the paper, the authors introduce a matrix-parametrized generalization of the multinomial probability mass function that involves a ratio of several multivariate gamma functions. They show the logarithmic complete monotonicity of this generalization and derive new inequalities involving ratios of multivariate gamma functions.