Advertisement

Statistical Papers

, Volume 34, Issue 1, pp 167–173 | Cite as

Characterizations of gamma, inverse Gaussian, and negative binomial distributions via their length-biased distributions

  • A. N. Ahmed
  • A. M. Abouammoh
Notes

Abstract

A general form for characterizing inverse Gaussian and Wald distributions, based on their respective length-biased distributions, is introduced. Further results for characterizations of the gamma distribution, the negative binomial distribution and some mixtures of them by using their lengthbiased distributions are establised.

Key words

Length biased distribution Negative binomial distribution Gamma distribution Inverse Gaussain distribution Chi-square distribution Mixed distributions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahasnullah, M. and Kirmani, S. (1984). A characterization of Wald distribution. Naval Research Logistics Quarterly, Vol. 31, pp. 155–158.CrossRefMathSciNetGoogle Scholar
  2. Chikara, R. and Folks, J. (1977). The inverse Gaussian distribution as a lifetime model. Technometrics, Vol. 19, pp. 461–468.CrossRefGoogle Scholar
  3. Cox, D. (1962). Renewal Theory, Methuen and Co. Ltd.Google Scholar
  4. Gupta, R. and Keating, J. (1986). Relations for reliability measures under length-biased sampling. Scandinavian Journal of statistics 13, ppl 49–56.MathSciNetGoogle Scholar
  5. Khattree, R. (1989). Characterization of inverse-Gaussian and Gamma distributions through their length-biased distributions. IEEE. Trans. on Reliability, Vol. 38, No. 5, pp. 610–611.MATHCrossRefGoogle Scholar
  6. Patil, P. and Rao, R. (1977). The weighted distributions: A survey of their applications. In Applications in Statistics (ed. Krishnaiah, R.). North Holland, pp. 383–405.Google Scholar
  7. Ross, S. (1983). Stochastic Processes. John Wiley & Sons, Inc., New York.MATHGoogle Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • A. N. Ahmed
    • 1
  • A. M. Abouammoh
    • 1
  1. 1.Department of Statist. and O.R., College of ScienceKing Saud UniversityRiyadhSaudi Arabia

Personalised recommendations