Existence conditions of permanental and multivariate negative binomial distributions

Nathalie Eisenbaum ^[1] ; Franck Maunoury ^[2]
1. [1] Pierre and Marie Curie University
  
  Pierre and Marie Curie University
  
  París, Francia
2. [2] Université Denis Diderot (France)
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 2, 2017, págs. 4786-4820
Idioma: inglés
DOI: 10.1214/17-AOP1179
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Resumen
- 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.