A reinforcement-depletion urn model: A contiguity case

  • K. O. Bowman
  • L. R. Shenton


An urn contains balls ofs different colors. The problem of the reinforcement of a specified color and random depletion of balls has been considered by Bernard (1977,Bull. Math. Biol.,39, 463–470) and Shenton (1981,Bull. Math. Biol.,43, 327–340), (1983,Bull. Math. Biol.,45, 1–9). Here we consider a special relation between a reinforcement and depletion, leading to a hypergeometric distribution.


Contiguous factorials factorial series distributions hypergeometric distribution moments 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bernard, S. R. (1977). An urn model study of variability within a compartment,Bull. Math. Biol.,39, 463–470.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Johnson, N. L. and Kotz, S. (1970).Continuous Univariate Distributions—1, Houghton Mifflin Co., Boston.zbMATHGoogle Scholar
  3. [3]
    Kendall, M. G. and Stuart, A. (1969).The Advanced Theory of Statistics, Vol. 1, (3rd ed.), Charles Griffin & Co., London and High Wycombe; Hafner Press, New York.zbMATHGoogle Scholar
  4. [4]
    Shenton, L. R. (1981). A reinforcement-depletion urn problem—I. Basic theory,Bull. Math. Biol.,43, 327–340.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Shenton, L. R. (1983). A reinforcement-depletion urn problem—II. Application and generalization.Bull. Math. Biol.,45, 1–9.MathSciNetzbMATHGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1986

Authors and Affiliations

  • K. O. Bowman
    • 1
    • 2
  • L. R. Shenton
    • 1
    • 2
  1. 1.Oak Ridge National LaboratoryOak RidgeUSA
  2. 2.University of GeorgiaUSA

Personalised recommendations