, Volume 16, Issue 1, pp 27–31 | Cite as

Compound gamma, beta and F distributions

  • Satya D. Dubey


In this paper a compound gamma distribution has been derived by compounding a gamma distribution with another gamma distribution. The resulting compound gamma distribution has been reduced to the Beta distributions of the first kind and the second kind and to theF distribution by suitable transformations. This includes theLomax distribution as a special case which enjoys a useful property. Moment estimators for two of its parameters are explicitly obtained, which tend to a bivariate normal distribution. The paper contains expressions for a bivariate probability density function, its conditional expectation, conditional variance and the product moment correlation coefficient. Finally, all the parameters of the compound gamma distribution are explicitly expressed in terms of the functions of the moments of the functions of random variables in two different ways.


Gamma Distribution Conditional Expectation Beta Distribution Conditional Variance Gamma Probability 
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  1. Dubey, S. D.: Characterization Theorems for Several Distributions and their Applications. Journal of the Industrial Mathematics Society,16, 1966a, Part 1, 1–22.MathSciNetGoogle Scholar
  2. —— Transformations for Estimation of Parameters. Journal of the Indian Statistical Association,4, 1966b, Nos. 3 and 4, 109–124.MathSciNetGoogle Scholar
  3. Lomax, K. S.: Business failures: another example of the analysis of failure data. Jour. Amer. Stat. Assoc.,49, 1954, 847–852.zbMATHCrossRefGoogle Scholar

Copyright information

© Physica-Verlag 1970

Authors and Affiliations

  • Satya D. Dubey
    • 1
  1. 1.New York UniversityNew YorkU.S.A.

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