DMTCS

2005 International Conference on Analysis of Algorithms

Conrado Martínez (ed.)

DMTCS Conference Volume AD (2005), pp. 231-256


author: Guy Louchard, Helmut Prodinger and Mark Daniel Ward
title: The number of distinct values of some multiplicity in sequences of geometrically distributed random variables
keywords: Distinct values, geometric random variables, extreme value distribution
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.
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reference: Guy Louchard and Helmut Prodinger and Mark Daniel Ward (2005), The number of distinct values of some multiplicity in sequences of geometrically distributed random variables, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 231-256
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