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Estimation of Parameters on Some Extensions of the Katz Family of Discrete Distributions Involving Hypergeometric Functions

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A Modern Course on Statistical Distributions in Scientific Work

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 17))

Summary

A two-parameter family of discrete distributions developed by Katz (1963) is extended to three- and four-parameter families whose probability generating functions involve hypergeometric functions. This extension contains other distributions appearing in the literature as particular cases. Various methods of estimating the parameters are investigated and their asymptotic efficiency relative to maximum likelihood estimators compared.

This research was supported in part by the Wisconsin Alumni Research Foundation and by the Air Force Office of Scientific Research, AFOSR 72-236 3B.

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References

  1. Barankin, E. W. and Gurland, J. (1951). Univ. Calif. Pub. Statist. 1, 89–129.

    MathSciNet  Google Scholar 

  2. Crow, E. L. and Bardwell, G. E. (1963). Estimation of the parameters of the hyper-Poisson distributions in Classical and Contagious Discrete Distributions, G. P. Patil (ed.), Pergamon Press, New York, 127–140.

    Google Scholar 

  3. Dacey, M. F. (1972). Sankhyã Ser. B 34, 243–250.

    MathSciNet  Google Scholar 

  4. Good, I. J. (1953). Biometrika 40, 237–264.

    MathSciNet  MATH  Google Scholar 

  5. Hinz, P. and Gurland, J. (1970). J. Amer. Stat. Assoc. 65, 887–903.

    Article  MATH  Google Scholar 

  6. Irwin, J. O. (1963). Inverse factorial series as frequency distributions in Classical and Contagious Discrete Distributions, G. P. Patil (ed.), Pergamon Press, New York, 159–174.

    Google Scholar 

  7. Katz, L. (1963). Unified treatment of a broad class of discrete probability distributions in Classical and Contagious Discrete Distributions, G. P. Patil (ed.), Pergamon Press, New York, 175–182.

    Google Scholar 

  8. Kemp, A. W. (1968). Sankhyã Ser. A 30, 401–410.

    MathSciNet  MATH  Google Scholar 

  9. McGuire, J. V., Brindley, T. A. and Bancroft, T. A. (1957). Biometrics 13, 65–78.

    Article  Google Scholar 

  10. Neyman, J. (1939). Ann. Math. Stat. 10, 35–57.

    Article  MATH  Google Scholar 

  11. Ord, J. K. (1967). Biometrika, 54, 649–656.

    MathSciNet  MATH  Google Scholar 

  12. Simon (1954). Biometrika, 42, 425–440.

    Google Scholar 

  13. “Student” (1970). Biometrika 5, 351–360.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Wisconsin, Madison, Wisconsin, USA

    John Gurland & Ram Tripathi

Authors
  1. John Gurland
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  2. Ram Tripathi
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Editor information

Editors and Affiliations

  1. The Pennsylvania State University, University Park, Pa., USA

    G. P. Patil

  2. Temple University, Philadelphia, Pa., USA

    S. Kotz

  3. University of Warwick, Coventry, England

    J. K. Ord

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© 1975 D. Reidel Publishing Company, Dordrecht-Holland

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Gurland, J., Tripathi, R. (1975). Estimation of Parameters on Some Extensions of the Katz Family of Discrete Distributions Involving Hypergeometric Functions. In: Patil, G.P., Kotz, S., Ord, J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1842-5_6

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  • DOI: https://doi.org/10.1007/978-94-010-1842-5_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1844-9

  • Online ISBN: 978-94-010-1842-5

  • eBook Packages: Springer Book Archive

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