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A finite form for the wrapped Poisson distribution

Part of: Elementary classical functions Distribution theory - Probability Markov processes

Published online by Cambridge University Press:  01 July 2016

Frank Ball  and
Paul Blackwell
Frank Ball*
Affiliation:
University of Nottingham
Paul Blackwell*
Affiliation:
University of Sheffield
*
∗Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
∗∗Postal address: Department of Probability and Statistics, University of Sheffield, Sheffield S3 7RH, UK.
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Abstract

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We give a finite form for the probability mass function of the wrapped Poisson distribution, together with a probabilistic proof. We also describe briefly its connection with existing results.

MSC classification

Primary: 60E99: None of the above, but in this section
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 33B99: None of the above, but in this section
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 24 , Issue 1 , March 1992 , pp. 221 - 222
Copyright
Copyright © Applied Probability Trust 1992 

References

Bellman, R. (1960) Introduction to Matrix Analysis. McGraw-Hill, New York.Google Scholar
Blackwell, P. G. (1990) The Stochastic Modelling of Social and Territorial Behaviour. Unpublished PhD thesis, University of Nottingham.Google Scholar
Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes , 2nd edn. Academic Press, New York.Google Scholar
Kaufman, H. (1955) A bibliographical note on higher order sine functions. Scripta Math. 28, 29–36.Google Scholar
Lancaster, P. (1969) Theory of Matrices. Academic Press, New York.Google Scholar
Levy, P. (1939) L'addition des variables aléatoires défines sur une circonférence. Bull. Soc. Math. France 67, 1–41.Google Scholar
Mardia, K. V. (1972) Statistics of Directional Data. Academic Press, New York.Google Scholar