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On a generalization of the Rényi–Srivastava characterization of the Poisson law

Part of: Distribution theory - Probability Combinatorial probability Combinatorics Probability theory and stochastic processes Mathematical modeling, applications of mathematics

Published online by Cambridge University Press:  25 February 2021

Jean-Renaud Pycke
Jean-Renaud Pycke*
Affiliation:
University of Évry and University of Paris
*
*Postal address: University of Évry, LaMME, CNRSUMR 8071, 23 bvd de France, 91 037 Évry Cedex, France; University of Paris, Laboratory I3SP (URP 3625) Sports Faculty, France. Email address: [email protected]
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Abstract

We give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generalization of a characterization of Poisson law due to Rényi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions occurring in the extended collective model in non-life insurance.

Keywords

Poisson lawcompound variablesBell polynomialsnon-life insurance

MSC classification

Primary: 60E05: Distributions 60E10: Characteristic functions; other transforms 60C05: Combinatorial probability
Secondary: 05A17: Partitions of integers 60-08: Computational methods (not classified at a more specific level) 97M30: Financial and insurance mathematics
Type
Research Papers
Information
Journal of Applied Probability , Volume 58 , Issue 1 , March 2021 , pp. 68 - 82
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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