An axiomatic foundation for a multivariate measure of affinity among a number of distributions

The aim of this article is to give an axiomatic characterization of the multivariate measure of "affinity" among a number of distributions. This measure has been used in the last few years for statistical decision making. When there are only two distributions involved this measure of affinity is related to a measure of distance between the distributions. In this article the multivariate measure is characterized by a set of four axioms. It is shown that these axioms lead to a functional equation whose unique solution is the measure of affinity under consideration. The axioms are also intuitively appealing as desirable properties for a measure of affinity.