Axiomatic characterization of the $\chi^{2}$ dissimilarity measure

TL;DR

This paper provides an axiomatic foundation for the chi-squared dissimilarity measure by solving a generalized functional equation, offering a theoretical understanding of its properties.

Contribution

It introduces a novel axiomatic characterization of the chi-squared dissimilarity measure through a generalized functional equation.

Findings

Axiomatic basis for chi-squared dissimilarity established

Solution to a new generalized functional equation

Enhanced theoretical understanding of dissimilarity measure

Abstract

We axiomatically characterize the $\chi^{2}$ dissimilarity measure. To this end, we solve a new generalization of a functional equation discussed in Aczel (Lectures on functional equations and their applications, Academic Press, 1966).