The Open Mathematics, Statistics and Probability Journal

2009, 1 : 7-10
Published online 2009 January 15. DOI: 10.2174/1876527000901010007
Publisher ID: TOSPJ-1-7

Asymptotic Expansion for Inverse Moments of Binomial and Poisson Distributions

Marko ZnidariČ
Faculty of Mathematics and Physics University of Ljubljana, Slovenia.

ABSTRACT

An asymptotic expansion for inverse moments of positive binomial and Poisson distributions is derived. The expansion coefficients of the asymptotic series are given by the positive central moments of the distribution. Compared to previous results, a single expansion formula covers all (also non-integer) inverse moments. In addition, the approach can be generalized to other positive distributions.