A General Class of Coefficients of Divergence of One Distribution from Another

Let P1 and P2 be two probability measures on the same space and let 0 be the generalized Radon-Nikodym derivative of P2 with respect to P1. If C is a continuous convex function of a real variable such that the Pl-expectation (generalized as in Section 3) of C(+) provides a reasonable coefficient of the Pl-dispersion of 0, then this expectation has basic properties which it is natural to demand of a coefficient of divergence of P2 from P1. A general class of coefficients of divergence is generated in this way and it is shown that various available measures of divergence, distance, discriminatory information, etc., are members of this class.