International Journal of Mathematics and Mathematical Sciences 
Volume 10 (1987), Issue 3, Pages 597-607
doi:10.1155/S016117128700070X

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

Abstract

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.