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.