Inverse moments of univariate discrete distributions via the Poisson expansion

Details Inverse moments of univariate discrete distributions via the Poisson expansion Inverse moments of univariate discrete distributions via the Poisson expansion

2008-09-24

arxiv.org/abs/0809.4155v1

Mathematics

Statistics Theory

21 pages, 6 figures, 1 Mathematica program

Scientific paper

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.

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