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 language | English |
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Pages (from-to) | 607-613 |
Number of pages | 7 |
Journal | Statistics |
Volume | 20 |
Issue number | 4 |
DOIs | |
State | Published - Jan 1 1989 |
Keywords
- Stochastic urn model
- binomial distribution
- difference equations
- generalized negative binomial distribution
- negative binomial distribution