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THE ANALYSIS OF SINGLETONS IN GENERALIZED BIRTHDAY PROBLEMS

Published online by Cambridge University Press:  27 April 2012

Matthijs R. Koot  and
Michel Mandjes
Matthijs R. Koot
Affiliation:
Informatics Institute, University of Amsterdam, The Netherlands E-mail: koot@cyberwar.nl
Michel Mandjes
Affiliation:
Korteweg-de Vries Institute for Mathematics, University of Amsterdam, The Netherlands; Eurandom, Eindhoven University of Technology, The Netherlands CWI, Amsterdam, The Netherlands E-mail: m.r.h.mandjes@uva.nl
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Abstract

This paper describes techniques to characterize the number of singletons in the setting of the generalized birthday problem, that is, the birthday problem in which the birthdays are non-uniformly distributed over the year. Approximations for the mean and variance presented which explicitly indicate the impact of the heterogeneity (expressed in terms of the Kullback–Leibler distance with respect to the homogeneous distribution). Then an iterative scheme is presented for determining the distribution of the number of singletons. The approximations are validated by experiments with demographic data.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 2 , April 2012 , pp. 245 - 262
Copyright
Copyright © Cambridge University Press 2012

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