EXPANSIONS FOR MOMENTS OF COMPOUND POISSON DISTRIBUTIONS

摘要

Expansions for moments of X, the mean of a random sample of size n, are given for both the univariate and multivariate cases. The coefficients of these expansions are simply Bell polynomials. An application is given for the compound Poisson variable S_N, where S_n = nX and N is a Poisson random variable independent of X_1, X_2,..., yielding expansions that are computationally more efficient than the Panjer recursion formula and Grubbstroem and Tang's formula.