A Stochastic Urn Model for the Generalized Negative Binomial Distribution

Felix Famoye, P. C. Consul

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We discuss a stochastic urn model in which there are two urns A and B. B is originally empty and A contains some fixed number of white and black balls. A player selects integers n > 0 and β ⪴0. Balls are drawn with replacement in A and balls of the same color are put in B as long as the number of white balls in B exceeds (β−1) times the number of black balls in B. Under this condition, the player stops after drawing n +βx balls and is declared to be a winner if urn B has x black balls. This number of black balls, x, is shown to have the generalized negative binomial distribution.

Original languageEnglish
Pages (from-to)607-613
Number of pages7
JournalStatistics
Volume20
Issue number4
DOIs
StatePublished - Jan 1 1989

Keywords

  • Stochastic urn model
  • binomial distribution
  • difference equations
  • generalized negative binomial distribution
  • negative binomial distribution

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