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A Bivariate Hyper-Poisson Distribution

  • Munir Ahmad
Conference paper
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 79)

Summary

Bardwell and Crow (1964) introduce a two-parameter family of the univariate hyper-Poisson distributions covering the Poisson and the left truncated Poisson distributions as particular cases. In this paper, a bivariate hyper-Poisson distribution is derived with univariate hyper-Poisson distributions as its marginals and bivariate Poisson distribution as a particular case. Various other particular cases and some properties of the new bivariate distribution are discussed. The moment method has been employed to estimate the parameters.

Key Words

bivariate hyper-Poisson distribution confluent hypergeometric function method of moments 

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References

  1. Bardwell, G. F. and Crow, E. L. (1964). A two-parameter family of hyper-Poisson distributions. Journal of American Statistical Association, 59, 133–141.MathSciNetCrossRefMATHGoogle Scholar
  2. Crow, E. L. and Bardwell, G. F. (1963). Estimation of the parameters of the hyper-Poisson distributions. In Classical and Contagious Discrete Distributions, G. P. Patil, ed. Pergamon Press, New York. Pages 127–140.Google Scholar
  3. Gurland, J. and Tripathi, R. (1975). Estimation of parameters on some extensions of the Katz family of discrete distributions involving hypergeometric function. In Statistical Distributions in Scientific Work, Vol. I, G. P. Patil, ed. Reidel, Dordrecht-Holland. Pages 59–82.Google Scholar
  4. Katz, L. (1963). Unified treatment of a broad class of discrete probability distributions. In Classical and Contagious Discrete Distributions, Vol. I, G. P. Patil, ed. Pergamon Press, New York. Pages 175–182.Google Scholar
  5. Kendall, M. G. and Stuart, A. (1977). Advanced Theory of Statistics, Vol. 2, Distribution Theory ( fourth edition ). Griffin, London.Google Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Munir Ahmad
    • 1
  1. 1.University of Petroleum and MineralsDhahranSaudi Arabia

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