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Absorption sampling and the absorption distribution

Part of: Distribution theory - Probability Stochastic processes

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: [email protected]
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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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References

Bailey, W.N. (1935). Generalized Hypergeometric Series. Cambridge University Press, London.Google Scholar
Benkherouf, L., and Alzaid, A.A. (1993). On the generalized Euler distribution. Statistics and Probability Letters 18, 323–326.CrossRefGoogle Scholar
Blomqvist, N. (1952). On an exhaustion process. Skandinavisk Aktuarietidskrift 35, 201–210.Google Scholar
Borenius, G. (1953). On the statistical distribution of mine explosions. Skandinavisk Aktuarietidskrift 36, 151–157.Google Scholar
Dunkl, C.F. (1981). The absorption distribution and the q-binomial theorem. Commun. Statist. – Theory and Methods A10, 1915–1920.Google Scholar
Emlen, J.M. (1973). Ecology: An Evolutionary Approach. Addison-Wesley, Reading, MA.Google Scholar
Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. (1953). Higher Transcendental Functions I, McGraw-Hill, New York.Google Scholar
Gasper, G., and Rahman, M. (1990). Basic Hypergeometric Series. Cambridge University Press, Cambridge.Google Scholar
Johnson, N.L., Kotz, S., and Kemp, A.W. (1992). Univariate Discrete Distributions, 2nd edn. Wiley, New York.Google Scholar
Kemp, A.W., and Kemp, C.D. (1991). Weldon's dice data revisited. Amer. Statistician 45, 216–222.Google Scholar
Kemp, A.W., and Newton, J. (1990). Certain state-dependent processes for dichotomised parasite populations. J. Appl. Prob. 27, 251–258.Google Scholar
Rawlings, D. (1997). Absorption processes: models for q-identities. Adv. in Appl. Math. 18, 133–148.CrossRefGoogle Scholar
Slater, L.J. (1966). Generalized Hypergeometric Functions. Cambridge University Press, London.Google Scholar