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The generalized hypergeometric family of distributions

  • Masaaki Sibuya
  • Ryoichi Shimizu
Article

Summary

This is an expository summary of the authors' report on classification of the generalized hypergeometric (GHg for short) family of distributions (Sibuya and Shimizu (1981),Keio Science and Technology Report, to appear). Emphasis is laid on the definition of the distributions based on some conventional rules, and on the complete classification of the multivariate GHg distributions, whose types are found to be rather limited in spite of their quite general definition. Previous classifications and namings are summarized and compared with the new one.

Keywords

Conditional Distribution Distribution Range Beta Variable Negative Binomial Distribution Probability Parameter 

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References

  1. [1]
    Janardan, K. G. (1973). Chance mechanisms for multivariate hypergeometric models,Sankhyà, A,35, 465–478.zbMATHGoogle Scholar
  2. [2]
    Janardan, K. G. and Patil, G. P. (1972). A unified approach for a class of multivariate hypergeometric models,Sankhyà, A,34, 363–376.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Janardan, K. G. and Schaeffer, D. J. (1977). A generalization of Markov-Pólya distributions, its extensions and applications,Biometrical J.,19, 87–106.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Kemp, C. D. and Kemp, A. W. (1956). Generalized hypergeometric distributions,J. Roy. Statist. Soc., B,18, 202–211.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Sibuya, M. and Shimizu, R. (1981). Classification of the generalized hypergeometric family of distributions,Keio Science and Technology Report, to appear.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1981

Authors and Affiliations

  • Masaaki Sibuya
    • 1
  • Ryoichi Shimizu
    • 1
  1. 1.Tokyo Scientific Center, IBM JapanThe Institute of Statistical MathematicsTokyoJapan

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