Divergence Measures and Characterization of Probability Distributions

One of the important issues in applications of statistics and probability is finding appropriate probabilistic metrics of distance or difference or affinity between probability distributions. A number of divergence/information measures have been proposed. Some measures like Kullback-Leibler divergence, variation distance, Hellinger distance, chi square divergence, Bhattacharyya distance, Harmonic distance, Jaffrey's distance, Triangular discrimination have been applied in a variety of disciplines. The maximum-entropy principle (MEP) and the minimum cross-entropy principle (MCEP) have been applied successfully in different fields such as biology, medicine, agriculture, economics, finance, insurance, accountancy, marketing, elections, regional and urban planning, transportation, statistics, thermodynamics, spectral analysis, image reconstruction, pattern recognition, operations research, science and engineering. MCEP is based on minimization of the Kullback divergence measure. My research primarily aims at generalizing divergence measures and their characterizations with applications to the probability distributions.

[10] P. Kumar and A. Johnson, “On A Symmetric Divergence Measure and Information Inequalities”. Journal of Inequalities in Pure and Appl. Math., 6, 3, pp. 1-13, 2005. ( pdf )

[9] Pranesh Kumar andI. J. Taneja, “On Unified Generalizations of Relative Jenson-Shannon and Arithmetic-Geometric Divergence Measures and Their properties”. Ind. Jour. Math. and Math. Sc., 1, 1, pp. 77-97, 2005. ( pdf )

[8] Pranesh Kumar and Susan Chinna, “A Symmetric Information Divergence Measure of the Csiszar’s f-Divergence Class”. Computers and Mathematics with Applications, 49, pp. 575-88, 2005. ( pdf )

[7] Pranesh Kumar and Laura Hunter, “Information Divergence Measures and Information Inequalities”. Carpathian Jour. Math., 20,1, pp.51-66, 2004. ( pdf )

[6] I.J.Taneja and Pranesh Kumar, “Relative Information of Type s, Csiszar's f-Divergence, and Information Inequalities”. Information Sciences, 166, pp.105-125, 2004. ( pdf )

[5] P. Kumar, “Minimum Chi Square Divergence Principle and Its Applications to Exponential Probability Distributions”. (preprint) ( pdf )

[4] P. Kumar and I.J. Taneja, “Chi Square Divergence and Minimization Problem for Continuous Probability Distributions”. (preprint) ( pdf )

[3] P. Kumar and I.J. Taneja, “Chi Square Divergence and Minimization Problem”. (preprint) ( pdf )

[2] I.J. Taneja and P. Kumar, “Generalized Non-Symmetric Divergence Measures and Inequalities”. (preprint) ( pdf )

[1] P. Kumar, “Characterizations of Beta Probability Distributions Based on the Minimum Chi Square Divergence Principle”. (preprint) ( pdf )