Cumulants of Convolution—Mixed Distributions

1 January 1977

journal article
research article
Published by Cambridge University Press (CUP) in ASTIN Bulletin

Vol. 9 (1-2) , 59-63
https://doi.org/10.1017/s0515036100011387

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 that and If P_r represents the probability that exactly r claims occur in the period, then Kupper [4] has shown on certain simplifying assumptions that where , the probability of exactly r claims in n accidents, is given by and for γ < nFurther

Keywords

PR REPRESENTS
STOCHASTIC VARIABLES
CLAIMS OCCUR
RISK PROCESS
VARIABLE DENOTING
SIMPLIFYING ASSUMPTIONS
MIXED DISTRIBUTIONS
TOTAL LOSS
DISTRIBUTIONS CONSIDER
RANDOM VARIABLE

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