Abstract
Matusita ([5]-[8]) introduced and discussed measures of 'aff ini ty ' and ' distance' between two statistical populations. This article is mainly concerned with two types of characterizations of 'aff ini ty ' and ' dist ance ' when the populations are discrete. One is based on a recurrence relation and the other deals with a maximization principle. By using the main results obtained in this article, characterization theorems are also given for Bhattacharyya's measure of distance ([1], [2]), Jeffreys' measure of invariance ([1], [3]), Pearson's measure of discrepancy [1] and a generalized measure of dispersion introduced by Mathai [4]. Alternate definitions of 'affinity ' and 'dis tance, ' as solutions of certain functional equations, are also suggested in this article. Consider two discrete distributions given by the probabilities,
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