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

Ouimet, Frédéric and Qi, Feng (2021) Logarithmically complete monotonicity of a matrix-parametrized analogue of the multinomial distribution. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220104-233133058

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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 new inequalities involving ratios of multivariate gamma functions.

Item Type:

Report or Paper (Discussion Paper)

Related URLs:

URL	URL Type	Description
http://arxiv.org/abs/2105.01494	arXiv	Discussion Paper

ORCID:

Author	ORCID
Ouimet, Frédéric	0000-0001-7933-5265

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 declare no conflict of interest. The authors contributed equally to this work. All authors read and approved the final manuscript.

Funders:

Funding Agency	Grant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)	UNSPECIFIED
Fonds de recherche du Québec - Nature et technologies (FRQNT)	B3X

Subject Keywords:

complete monotonicity, logarithmically complete monotonicity, ratio, multivariate gamma function, multinomial distribution, matrix-variate Dirichlet distribution, positive definite matrix, inequality

Classification Code:

2020 MSC: Primary 26A48; Secondary 05A20, 11B57, 26A51, 33B15, 44A10, 60E05, 60E10, 62E15

Record Number:

CaltechAUTHORS:20220104-233133058

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20220104-233133058

Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

112700

Collection:

CaltechAUTHORS

Deposited By:

George Porter

Deposited On:

05 Jan 2022 16:12

Last Modified:

05 Jan 2022 16:12

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