Approximation and estimation of some compound distributions
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 \textit{P. Embrechts}, \textit{M. Maejima} and \textit{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.
applications to premium calculation principles
scientific article; zbMATH DE number 3934276