Probabilistic transforms for combinatorial urn models

O. Milenkovic, K. J. Compton

Research output: Contribution to journalArticle

Abstract

In this paper, we present several probabilistic transforms related to classical urn models. These transforms render the dependent random variables describing the urn occupancies into independent random variables with appropriate distributions. This simplifies the analysis of a large number of problems for which a function under investigation depends on the urn occupancies. The approach used for constructing the transforms involves generating functions of combinatorial numbers characterizing the urn distributions. We also show, by using Tauberian theorems derived in this paper, that under certain simple conditions the asymptotic expressions of target functions in the transform domain and in the inverse-transform domain are identical. Therefore, asymptotic information about certain statistics can be obtained without evaluating the inverse transform.

Original languageEnglish (US)
Pages (from-to)645-675
Number of pages31
JournalCombinatorics Probability and Computing
Volume13
Issue number4-5
DOIs
StatePublished - Jul 1 2004
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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