International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 597-607

A measure of mutual divergence among a number of probability distributions

J. N. Kapur,1 Vinod Kumar,2 and Uma Kumar2

1Department of Mathematics, Indian Institute of Technology, New Delhi 110016, India
2School of Business, Carleton University, Ottawa K1S 5B6, Canada

Received 11 September 1985; Revised 22 September 1986

Copyright © 1987 J. N. Kapur et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The principle of optimality of dynamic programming is used to prove three major inequalities due to Shannon, Renyi and Holder. The inequalities are then used to obtain some useful results in information theory. In particular measures are obtained to measure the mutual divergence among two or more probability distributions.