The Annals of Probability

Existence conditions of permanental and multivariate negative binomial distributions

Nathalie Eisenbaum and Franck Maunoury

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Abstract

Existence conditions of permanental distributions are deeply connected to existence conditions of multivariate negative binomial distributions. The aim of this paper is twofold. It answers several questions generated by recent works on this subject, but it also goes back to the roots of this field and fixes existing gaps in older papers concerning conditions of infinite divisibility for these distributions.

Article information

Source
Ann. Probab., Volume 45, Number 6B (2017), 4786-4820.

Dates
Received: December 2015
Revised: January 2017
First available in Project Euclid: 12 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aop/1513069273

Digital Object Identifier
doi:10.1214/17-AOP1179

Mathematical Reviews number (MathSciNet)
MR3737924

Zentralblatt MATH identifier
1385.60049

Subjects
Primary: 60G15: Gaussian processes 60E05: Distributions: general theory 60E07: Infinitely divisible distributions; stable distributions 60E10: Characteristic functions; other transforms 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14] 15B48: Positive matrices and their generalizations; cones of matrices

Keywords
Permanental vector negative binomial distribution $M$-matrix Gaussian vector matrix cycles permanent determinant infinite divisibility

Citation

Eisenbaum, Nathalie; Maunoury, Franck. Existence conditions of permanental and multivariate negative binomial distributions. Ann. Probab. 45 (2017), no. 6B, 4786--4820. doi:10.1214/17-AOP1179. https://projecteuclid.org/euclid.aop/1513069273


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