Distribution Theory

Abstract

Much of classical statistical inference for linear models is based on special cases of those models for which the response vector y has a multivariate normal distribution. Before we can present those inferential methods, therefore, we must first precisely define the multivariate normal distribution and the related noncentral chi-square, t, and F distributions, and describe some of their important properties. These are the topics of this chapter. It is possible to extend some of the results presented in this chapter and in the remainder of the book to linear models in which y has a distribution from the more general family of “elliptical” distributions, but we do not consider these extensions here. The reader who is interested in such extensions is referred to Ravishanker and Dey (A first course in linear model theory. Chapman & Hall/CRC Press, Boca Raton, 2002) and Harville (Linear models and the relevant distributions and matrix algebra. CRC Press, Boca Raton, 2018).