The number of distinct values of some multiplicity in sequences of geometrically distributed random variables

Guy Louchard 1 Helmut Prodinger 2 Mark Daniel Ward 3
1 ULB - Département d'Informatique [Bruxelles]
2 DMS - Department of Mathematical Sciences [Matieland, Stellenbosch Uni.]
3 Department of mathematics Purdue University
Abstract : We consider a sequence of $n$ geometric random variables and interpret the outcome as an urn model. For a given parameter $m$, we treat several parameters like what is the largest urn containing at least (or exactly) $m$ balls, or how many urns contain at least $m$ balls, etc. Many of these questions have their origin in some computer science problems. Identifying the underlying distributions as (variations of) the extreme value distribution, we are able to derive asymptotic equivalents for all (centered or uncentered) moments in a fairly automatic way.
Keywords : extreme value distribution Distinct values geometric random variables
Type de document :
Communication dans un congrès
Conrado Martínez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.231-256, 2005, DMTCS Proceedings
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Guy Louchard, Helmut Prodinger, Mark Daniel Ward. The number of distinct values of some multiplicity in sequences of geometrically distributed random variables. Conrado Martínez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.231-256, 2005, DMTCS Proceedings. 〈hal-01184030〉

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