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Published July 2022 | public
Journal Article

Logarithmically complete monotonicity of a matrix-parametrized analogue 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 logarithmically complete monotonicity of this generalization and derive several inequalities involving ratios of multivariate gamma functions.

Additional Information

The authors thank Gérard Letac (Institut de Mathématiques de Toulouse, Université Paul Sabatier, France; gerard.letac@math.univ-toulouse.fr) for providing the third proof of Lemma 2.1. F. Ouimet was supported by postdoctoral fellowships from the NSERC (PDF) and the FRQNT (B3X supplement). Data availability statement. No data were used to support this study. The authors contributed equally to this work. All authors read and approved the final manuscript. The authors declare no conflict of interest.

Additional details

Created:
August 22, 2023
Modified:
October 24, 2023