Remarks on the non-identifiability of mixtures of distributions

  • Khalaf E. Ahmad
  • Essam K. Al-Hussaini


This note points out some observations regarding the non-identifiability of finite mixtures of beta and Pearson Type VI distributions.


Hull Convex Hull Beta Distribution Beta Function Borel Subset 


  1. [1]
    Al-Hussaini, E. K. and Ahmad, K. E. (1981). On the identifiability of finite mixtures of distributions,IEEE Trans. Inf. Theory, IT-27, 664–668.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Blum, J. R. and Susarla, V. (1977). Estimation of a mixing distribution,Ann. Prob.,5, 201–209.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Bremner, J. M. (1978). Mixtures of beta distributions. Algorithm AS 123,Appl. Statist.,27, 104–109.CrossRefGoogle Scholar
  4. [4]
    Robbins, H. (1964). The empirical Bayes approach to statistical decision problems,Ann. Math. Statist.,35, 1–20.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Teicher, H. (1960). On the mixture of distributions,Ann. Math. Statist.,31, 55–73.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Teicher, H. (1963). Identifiability of finite mixtures,Ann. Math. Statist.,34, 1265–1269.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Tretter, Marietta J. and Walster, William J. (1975). Central and noncentral distributions of Wilks statistic in MANOVA as mixtures of incomplete beta functions,Ann. Statist.,3, 467–472.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Yakowitz, S. J. and Spragins, J. D. (1968). On the identifiability of finite mixtures,Ann. Math. Statist.,39, 209–214.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1982

Authors and Affiliations

  • Khalaf E. Ahmad
    • 1
  • Essam K. Al-Hussaini
    • 1
  1. 1.University of AssiutAssiutEgypt

Personalised recommendations