Asymptotic Expansion for Inverse Moments of Binomial and Poisson Distributions

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

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© 2009 ZnidariČ et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Faculty of Mathematics and Physics University of Ljubljana, Slovenia. E-mail:


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.