The Annals of Probability

Existence conditions of permanental and multivariate negative binomial distributions

Nathalie Eisenbaum and Franck Maunoury

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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

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

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

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Zentralblatt MATH identifier

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

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


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.

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