A simple proof of Feller's characterization of the compound Poisson distributions
type: Item
instance of: scholarly article
title: A simple proof of Feller's characterization of the compound Poisson distributions
zbMATH Open document ID: 0614.62010
DOI: 10.1016/0167-6687(87)90008-4
author: A. Valderrama Ospina
author: H. U. Gerber
published in: Insurance Mathematics \& Economics
publication date: 1987-01-01T00:00:00Z
review text: A classical result of \textit{W. Feller} [An introduction to probability theory and its applications. Vol. 1, 3rd ed. (1968; Zbl 0155.231)] is that every distribution that is infinitely divisible and concentrated on the non-negative integers is compound Poisson. We give a simple proof that uses some of the recursive formulas that have recently become popular among actuaries.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 3994728
zbMATH Keywords: characterization
zbMATH Keywords: Feller's theorem
zbMATH Keywords: infinitely divisible
zbMATH Keywords: compound Poisson
zbMATH Keywords: recursive formulas
MaRDI profile type: Publication
full work available at URL: 0167-6687(87)90008-4
OpenAlex ID: W2053808587
cites work: Recursive formulas for discrete distributions
cites work: Q5538132
description: scientific article; zbMATH DE number 3994728