Summary
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.
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References
Bad Dumitrescu, M. (1984). The minimum cross-entropy estimation of a parameter,Bull. Math. Soc. Sci. Math. Roum., 28,4, 291–297.
Guiaşu, S. (1977).Information Theory with Applications, McGraw-Hill, New York.
Jaynes, E. T. (1957). Information theory and statistical mechanics,Phis. Rev.,106, 620–630,108, 171–182.
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.
Kulback, S. and Leibler, R. A. (1951). On information and sufficiency,Ann. Math. Statist.,22, 79–86.
Kullback, S. (1959). Information Theory and Statistics, Wiley, New York.
Kullback, S. and Khairat, M. A. (1966). A note on minimum discriminatin information,Ann. Math. Statist.,37, 279–280.
Preda, V. (1982). The Student distribution and the principle of maximum entropy,Ann. Inst. Statist. Math.,34, 335–338.
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.
Shore, J. E. and Johnson, R. W. (1981). Properties of cross-entropy minimization,IEEE Trans. Inf. Theory, IT,27, no. 4, 472–482.
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Bad Dumitrescu, M.E. The application of the principle of minimum cross-entropy to the characterization of the exponential-type probability distributions. Ann Inst Stat Math 38, 451–457 (1986). https://doi.org/10.1007/BF02482532
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DOI: https://doi.org/10.1007/BF02482532