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Inequalities for multinomial allocations with application to DNA fingerprinting

Part of: Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Sergei Grishechkin
Sergei Grishechkin*
Affiliation:
Moscow State University
*
∗Postal address: Warshavskoje shosse, d.88, kv.43, Moscow 113556, Russia. Email address: serge@star.net
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Abstract

We consider an allocation of n balls into N cells according to probabilities pi. Assuming that the balls are allocated successively, denote by φ(n,N) the number of such balls which go into an already occupied cell. If n = 2 the probability that two balls will occupy the same cell is equal to the so-called match probability MP = p21 + … + p2N. An upper estimate for the probability ℙ(φ(n,N) ≤ m) which depends only on n and MP is derived. Such inequalities are important for estimation of the reliability of DNA fingerprinting, a new method of crime investigation which is currently much debated.

Keywords

Random allocationsPoisson approximation

MSC classification

Primary: 60C05: Combinatorial probability
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 707 - 717
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

This work supported by the Russian Foundation for Basic Research, grant 95–0099 and the Russian Human Scientific Foundation, grant 96-03-04379.

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