1999•Communication in Statistics- Theory and MethodsRequires access

Moments and generating functions for the absortion distribution and its negative binomial analogue

Martin J. Newby

Abstract

The moments of the absorption are difficult to obtain. The generating functions are basic hypergeometric functions. This paper shows how to define two shift operators that allow elementary arguments to be used to develop recursions for the expected values of general functions. The exact moments of the distribution follow. The generating function for the negative binomial analogue gives the moments directly.

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Key concepts: Hypergeometric function, Hypergeometric distribution, Binomial (polynomial), Negative binomial distribution, Mathematics, Generating function, Reliability (semiconductor), Distribution (mathematics)