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An order statistic characterization of the poisson renewal process

Published online by Cambridge University Press:  14 July 2016

Uri Liberman
Uri Liberman*
Affiliation:
Tel-Aviv University
*
∗Postal address: Department of Statistics, Tel-Aviv University, Ramat-Aviv, Israel
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Abstract

Using the characterization of point processes having the order statistic property we prove that the only renewal process that has the order statistic property is the Poisson process.

Keywords

ORDER STATISTIC PROPERTYPOINT PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 717 - 722
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research supported in part by NIH grants GM 28016 and GM 10452.

References

Bailey, N. T. J. (1961) Introduction to the Mathematical Theory of Genetic Linkage. Clarendon Press, Oxford.Google Scholar
Cox, D. R. (1970) Renewal Theory. Methuen, London.Google Scholar
Crump, K. (1975) On point processes having an order statistic property. Sankhya A37, 396–404.Google Scholar
Feigin, P. D. (1979) On the characterization of point processes with the order statistic property. J. Appl. Prob. 16, 297–304.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and Its Applications, Vol. 2. Wiley, New York.Google Scholar
Jennings, H. S. (1923) The numerical relations in the crossing over of the genes with a critical examination of the theory that genes are arranged in a linear series. Genetics 8, 393–457.CrossRefGoogle Scholar
Karlin, S. and Liberman, U. (1979) A natural class of multilocus recombination processes and related measures of crossover interference. Adv. Appl. Prob. 11, 479–501.Google Scholar
Nawrotzki, K. (1962) Eine Grenzwertsatz für homogene zufällige Punktfolgen. Math. Nachr. 24, 201–217.Google Scholar
Owen, A. R. G. (1950) The theory of genetical recombination. Adv. Genet. 3, 111–157.Google Scholar