| 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 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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