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Approximation and estimation of some compound distributions. (English) Zbl 0583.62091
With \(p_ n\) as the probability of the occurrence of n claims and F(x) as the distribution of claim size the function \[ 1- G(x)=\sum^{\infty}_{n=1}p_ n\{1-F^{(n)}(x)\} \] is used for approximations of some classes of claim processes based on asymptotic results by P. Embrechts, M. Maejima and E. Omey, Ann. Probab. 12, 561-570 (1984; Zbl 0537.60087) and others. The results are applied to the Poisson case, the Pascal case and the compound Poisson model.
Reviewer: Ch.Netzel

MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
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