Difference equation approaches in evaluation of compound distributions
type: Item
instance of: scholarly article
title: Difference equation approaches in evaluation of compound distributions
zbMATH Open document ID: 0613.62020
DOI: 10.1016/0167-6687(87)90006-0
published in: Insurance Mathematics \& Economics
publication date: 1987-01-01T00:00:00Z
review text: The second author [Astin Bull. 12, 22-26 (1981)], \textit{B. Sundt} and \textit{W. Jewell} [ibid. 12, 27-39 (1981)] and the authors [ibid. 13, 1-11 (1982)] derive computational formulae for the density of the compound distribution when the frequency distribution satisfies certain difference equations. In many instances restrictions are placed on the severity distribution. In this paper it is shown how the results may be adapted to a wider class of severity distributions, including the inverse Gaussian and the Pareto distribution (among others). The computational techniques are clarified and in some cases simplified, and an additional class of frequency distributions is considered, which contains some other well-known distributions. It is then shown how the results may be extended to some well-known contagious frequency distributions such as the Neyman class.
Mathematics Subject Classification ID: 62E99
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 3992629
zbMATH Keywords: compound distribution
zbMATH Keywords: severity distributions
zbMATH Keywords: inverse Gaussian
zbMATH Keywords: Pareto distribution
zbMATH Keywords: contagious frequency distributions
zbMATH Keywords: Neyman class
author: Gordon E. Willmot
author: Harry H. Panjer
MaRDI profile type: Publication
full work available at URL: 0167-6687(87)90006-0
OpenAlex ID: W2044967912
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description: scientific article; zbMATH DE number 3992629