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Poisson approximation of multivariate Poisson mixtures

Part of: Distribution theory - Probability Distribution theory Limit theorems

Published online by Cambridge University Press:  14 July 2016

Bero Roos
Bero Roos*
Affiliation:
Universität Hamburg
*
∗ Postal address: Fachbereich Mathematik, SPST, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany. Email address: roos@math.uni-hamburg.de
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Abstract

We show how good multivariate Poisson mixtures can be approximated by multivariate Poisson distributions and related finite signed measures. Upper bounds for the total variation distance with applications to risk theory and generalized negative multinomial distributions are given. Furthermore, it turns out that the ideas used in this paper also lead to improvements in the Poisson approximation of generalized multinomial distributions.

Keywords

Finite signed measuregeneralized compound mixed Poisson distributiongeneralized multinomial distributiongeneralized negative multinomial distributionmultivariate Poisson approximationmultivariate Poisson mixturerisk theorytotal variation distanceupper bound

MSC classification

Primary: 60E05: Distributions
Secondary: 62E17: Approximations to distributions (nonasymptotic) 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 2 , June 2003 , pp. 376 - 390
Copyright
Copyright © Applied Probability Trust 2003 

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