Some Recent Advances with Power Series Distributions

  • S. W. Joshi
Conference paper
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 17)


Some recent results in power series distributions (psd’s on the following topics are discussed: (i) minimum variance unbiased estimation, (ii) elementary integral expressions for the distribution function, and (iii) sum-symmetric powers series distributions which is a multivariate extension of univariate psd’s.

Key Words

Power series distributions minimum variance unbiased estimation integral expressions distribution function tail probabilities truncated power series distributions Hermite distribution binomial distribution Poisson distribution negative binomial distribution logarithmic distribution sum-symmetric power series distributions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ahuja, J. C. and Enneking, E. A. (1972). J. Amer. Stat. Assoc. 67, 232.zbMATHCrossRefGoogle Scholar
  2. [2]
    Johnson, N. L. (1959). Biometrika 46, 352–363.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Joshi, S. W. Integral expressions for the tail probabilities of the power series distributions. (To appear in Sankhya.)Google Scholar
  4. [4]
    Joshi, S. W. and Park, C. J. (1974). Minimum variance unbiased estimation for truncated power series distributions. Sankhyã Ser A, in press.Google Scholar
  5. [5]
    Joshi, S. W. and Patil, G. P. (1971). Sankhya Ser A, J33, 175–184.MathSciNetzbMATHGoogle Scholar
  6. [6]
    Joshi, S. W. and Patil, G. P. (1972). Sankhya Ser A, 34, 377–386.MathSciNetzbMATHGoogle Scholar
  7. [7]
    Kemp, C. D. and Kemp, A. W. (1965). Biometrika 52, 381–394.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Kosambi, D. D. (1949). Proc. National Inst. Sci. India 15, 109–113.MathSciNetGoogle Scholar
  9. [9]
    Noack, A. (1950). Ann. Math. Statist. 21, 127–132.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    Patil, G. P. (1959). Contributions to estimation in a class of discrete distributions. Ph.D. Thesis, University of Michigan, Ann Arbor, Michigan.Google Scholar
  11. [11]
    Patil, G. P. (1961). Sankhyã 23, 269–280.MathSciNetzbMATHGoogle Scholar
  12. [12]
    Patil, G. P. (1962). Ann. Inst. Statist. Math. 14, 179–182.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    Patii, G. P. (1963). Ann. Math. Statist. 34, 1050–1056.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Patil, G. P. (1968). Sankhyã Ser B 30, 355–366.MathSciNetGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht-Holland 1975

Authors and Affiliations

  • S. W. Joshi
    • 1
  1. 1.Department of MathematicsUniversity of Texas at AustinUSA

Personalised recommendations