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Absorption sampling and the absorption distribution

Part of: Stochastic processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Adrienne W. Kemp
Adrienne W. Kemp*
Affiliation:
University of St Andrews
*
∗Postal address: School of Mathematical and Computational Sciences, The Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland. E-mail address: awk@st-andrews.ac.uk
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Abstract

The inverse absorption distribution is shown to be a q-Pascal analogue of the Kemp and Kemp (1991) q-binomial distribution. The probabilities for the direct absorption distribution are obtained via the inverse absorption probabilities and exact expressions for its first two factorial moments are derived using q-series transformations of its probability generating function. Alternative models for the distribution are given.

Keywords

Absorption distributioninverse absorption distributionq-Pascal distributionq-seriesbasic hypergeometric distributionsbirth-death processhesitant random walk

MSC classification

Primary: 60E99: None of the above, but in this section
Secondary: 60G99: None of the above, but in this section
Type
Short Communications
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 489 - 494
Copyright
Copyright © Applied Probability Trust 1998 

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