A General Class of Coefficients of Divergence of One Distribution from Another
- 1 January 1966
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 28 (1) , 131-142
- https://doi.org/10.1111/j.2517-6161.1966.tb00626.x
Abstract
Let p1 and p2 be two probability measures on the same space and let φ 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 p1‐expectation (generalized as in Section 3) of C(φ) provides a reasonable coefficient of the p1‐dispersion of φ, 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.This publication has 2 references indexed in Scilit:
- Association between Random Variables and the Dispersion of a Radon–Nikodym DerivativeJournal of the Royal Statistical Society Series B: Statistical Methodology, 1965
- A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of ObservationsThe Annals of Mathematical Statistics, 1952