Domain of existence of the Laplace transform of negative multinomial distributions and simulations
type: Item
instance of: scholarly article
title: Domain of existence of the Laplace transform of negative multinomial distributions and simulations
author: Philippe Bernardoff
published in: Statistics \& Probability Letters
publication date: 2022-12-08T00:00:00Z
review text: A probability distribution \( \sum_{\boldsymbol{\alpha} \in \mathbb{N}^n} p_{\boldsymbol{\alpha}}\delta_{\boldsymbol{\alpha}}\) on the set of nonnegative integers \(\mathbb{N}^n\) is said to be a negative multinomial distribution if there exists an affine polynomial \(P(z_1,\dots , z_n)\) and \(\lambda >0\) such that \[ \sum_{\boldsymbol{\alpha} \in \mathbb{N}^n} p_{\boldsymbol{\alpha}} z_1^{\alpha_1}\, \dots z_n^{\alpha_n} =\left(P(z_1,\dots , z_n)\right)^{-\lambda}. \] In [Bernoulli 9, No. 5, 877--893 (2003; Zbl 1065.60012)] the same author characterized all affine polynomials \(P\) which give rise to probability generating functions for infinitely divisible negative multinomial distributions. In this paper the author uses this characterization to derive the domain of existence of their Laplace transforms. As an application of these results, the author provides a construction and a simulation of these distributions in dimension 2.
reviewed by: Italo Simonelli
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 7629091
zbMATH Keywords: infinitely divisible distribution
zbMATH Keywords: negative multinomial distribution
zbMATH Keywords: probability generating function
zbMATH Keywords: Laplace transform
describes a project that uses: R
MaRDI profile type: Publication
full work available at URL: j.spl.2022.109709
OpenAlex ID: W4287162130
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DOI: 10.1016/J.SPL.2022.109709
description: scientific article; zbMATH DE number 7629091