The application of the principle of minimum cross-entropy to the characterization of the exponential-type probability distributions

  • Monica E. Bad Dumitrescu


Systematic and simple characterizations are presented for several familiar distributions in exponential family by means of the principle of minimum cross-entropy (minimum discrimination information). The suitable prior distributions and the appropriate constraints on expected values are given for the underlying distributions.

Key words

Minimum cross-entropy exponential distribution 


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  1. [1]
    Bad Dumitrescu, M. (1984). The minimum cross-entropy estimation of a parameter,Bull. Math. Soc. Sci. Math. Roum., 28,4, 291–297.MathSciNetMATHGoogle Scholar
  2. [2]
    Guiaşu, S. (1977).Information Theory with Applications, McGraw-Hill, New York.MATHGoogle Scholar
  3. [3]
    Jaynes, E. T. (1957). Information theory and statistical mechanics,Phis. Rev.,106, 620–630,108, 171–182.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Kampé de Fériet, J. (1963). Théorie de l'Information. Principle du Maximum de l'Entropie et ses Appications à la Statistique et à la Mécanique, Publications du Laboratoire de Calcul de la Faculté e Sciences de l'Université de Lille, Lille.MATHGoogle Scholar
  5. [5]
    Kulback, S. and Leibler, R. A. (1951). On information and sufficiency,Ann. Math. Statist.,22, 79–86.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Kullback, S. (1959). Information Theory and Statistics, Wiley, New York.MATHGoogle Scholar
  7. [7]
    Kullback, S. and Khairat, M. A. (1966). A note on minimum discriminatin information,Ann. Math. Statist.,37, 279–280.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Preda, V. (1982). The Student distribution and the principle of maximum entropy,Ann. Inst. Statist. Math.,34, 335–338.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Shore, J. E. and Johnson, R. W. (1980). Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy.IEEE Trans. Inf. Theory, IT,26, no. 1, 26–37.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Shore, J. E. and Johnson, R. W. (1981). Properties of cross-entropy minimization,IEEE Trans. Inf. Theory, IT,27, no. 4, 472–482.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1986

Authors and Affiliations

  • Monica E. Bad Dumitrescu
    • 1
  1. 1.University of BucharestBucharestHungary

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