MUTUAL INFORMATION FOR THE MIXTURE OF TWO MULTIVARIATE NORMAL DISTRIBUTIONS

W. R. Javier (U. S. A.) and A. K. Gupta (U. S. A.)

Received February 24, 2008

References:

[1] T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 2nd ed., Wiley, 1984. [2] D. R. Brillinger, Some data analyses using mutual information, Braz. J. Probab. Stat. 18(2) (2004), 163-182. [3] H. Cramer, Mathematical Methods of Statistics, Princeton University Press, 1945. [4] Luc Devroye, Laszlo Györfi and Gabor Lugosi, A Probabilistic Theory of Pattern Recognition, Springer, 1996. [5] J.-L. Guerrero, Multivariate mutual information: sampling distribution with applications, Comm. Statist. Theory Methods 23(5) (1994), 1319-1339. [6] W. R. Javier and A. K. Gupta, Mutual information for the mixture of two widely separated multivariate normal distributions, 2006 (unpublished). [7] S. Kullback, Information Theory and Statistics, Dover, 1959. [8] A. Mood, F. Graybill and D. Boes, Introduction to the Theory of Statistics, 3rd ed., McGraw-Hill, 1963. [9] R. J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, 1982. [10] C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27 (1948), 379-423 and 623-656.

Keywords and phrases: mutual information, mixture of two normal distributions, normal linear forms, normal quadratics forms, moment generating functions, truncated normals, chi-square distribution, series expansion for