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A representation of a discrete distribution by its binomial moments

Published online by Cambridge University Press:  14 July 2016

Andreas Brandt ,
Manfred Brandt  and
Hannelore Sulanke
Andreas Brandt
Affiliation:
Humboldt-Universität zu Berlin
Manfred Brandt
Affiliation:
Humboldt-Universität zu Berlin
Hannelore Sulanke*
Affiliation:
Humboldt-Universität zu Berlin
*
∗Postal address: Sektion Mathematik, Humboldt-Universität zu Berlin, PSF 1297, 1086 Berlin, German Democratic Republic.
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Abstract

Let pk, k ≧ 0, be a probability distribution having finite binomial moments Br, r ≧ 0, and the probability generating function U(z) with a radius of convergence α (≧ 1). In this note explicit and recursive formulae are derived allowing computation of the pk in terms of the Br if α > 1. Ch. Jordan's formula, which holds if α > 2, turns out to be a special case.

Keywords

BINOMIAL MOMENTSPROBABILITY GENERATING FUNCTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 208 - 214
Copyright
Copyright © Applied Probability Trust 1990 

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References

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