A Study on Volume of Difference of Two Joint pdf′s, Focused on the Relation to Normal Theory LR Tests Lee, Kwangjin;
In this paper we explain that normal theory likelihood-ratio tests(z, t, . F) for mean(s) or variance(s) can be geometrically related to volume of difference of two joint pdf's. One is an estimated joint pdf under null parameter space and the other is an estimated joint pdf under full parameter space . For explanations, ‘distance between two distributions’ is defined. We study properties of it, and derive some results on the distance between two multivariate normal distributions.
distance between two distributions;z, t, , F-tests;ANOVA;LR-test;
Introduction to the Theory of Statistics (3rd Edition), 1974.