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Some properties of similar pairs

Published online by Cambridge University Press:  01 July 2016

Gunnar Blom  and
Lars Holst
Gunnar Blom*
Affiliation:
University of Lund
Lars Holst*
Affiliation:
Royal Institute of Technology, Stockholm
*
∗Postal address: Department of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden.
∗∗Postal address: Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden.
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Abstract

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In a given set, the elements are compared pairwise. The number W of similar pairs is studied, that is, the number of pairs with a certain property in common. Under certain conditions, W has, approximately, a Poisson distribution. Examples are considered connected with the birthday problem and with a circle problem involving DNA breakages.

Keywords

BIRTHDAY PROBLEMDISSOCIATED STATISTICSDNA BREAKAGESMULTINOMIAL DISTRIBUTIONPOISSON APPROXIMATION
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 941 - 944
Copyright
Copyright © Applied Probability Trust 1989 

References

Barbour, A. D. and Eagleson, G. K. (1983). Poisson approximation for some statistics based on exchangeable trials. Adv. Appl. Prob. 15, 585–600.Google Scholar
Barbour, A. D. and Eagleson, G. K. (1984) Poisson convergence for dissociated statistics. J. R. Statist. Soc. B 46, 397–402.Google Scholar
Cowan, R., Collis, C. M. and Crigg, G. W. (1987) Breakage of double-stranded DNA due to single-stranded nicking. J. Theor. Biol. 127, 229–246.Google Scholar
Cowan, R., Culpin, D. and Gates, D. (1990) Asymptotic results for a problem of DNA breakage. J. Appl. Prob. 27 (2).CrossRefGoogle Scholar
Holst, L. (1989) A circle covering problem and DNA breakage. Statist. Prob. Lett. 8 (2).Google Scholar
Schwartz, W. (1988) Approximating the birthday problem. Amer. Statistician 42, 195–196.Google Scholar