Inverse moments of univariate discrete distributions via the Poisson expansion
Abstract
Description
In this note we present a series expansion of inverse moments of a non-negative discrete random variate in terms of its factorial cumulants, based on the Poisson-Charlier expansion of a discrete distribution. We apply the general method to the positive binomial distribution and obtain a convergent series for its inverse moments with an error residual that is uniformly bounded on the entire interval 0<=p<=1.
21 pages, 6 figures, 1 Mathematica program
21 pages, 6 figures, 1 Mathematica program