Cumulants of Convolution—Mixed Distributions

Alan Brown

ASTIN Bulletin, 1977, vol. 9, issue 1-2, 59-63

Abstract: Consider a risk process which is characterised by three stochastic variables(1) the number of accidents, N,(2) the number of claims per accident, C, and(3) the amount of a claim, X.Let Y be a random variable denoting the total loss in a given period.Suppose thatandIf Pr represents the probability that exactly r claims occur in the period, then Kupper [4] has shown on certain simplifying assumptions thatwhere , the probability of exactly r claims in n accidents, is given byand for γ

Date: 1977
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