Gamma, Dirichlet, and F distributions

Abstract

This chapter introduces some basic probability distributions useful in statistics. The gamma distribution, in particular, is the building block of many other distributions such as chi-square, F, and Dirichlet. The Dirichlet distribution, as defined in Section 3.3, has the important physical interpretation of proportion of time waited in a Poisson process. However, it has other applications such as the distribution of spacing variables (v. Problem 3.5.3) and the distribution theory (v. Section 4.5) related to spherical distributions, which play an important role in robustness.