Noncentral and central chi-square, f and beta distribution functions as special cases of the distribution function of an indefinite quadratic form

Abstract

The distribution functions of central and noncentral chi-square, F and β random variables are expressed as special cases of the distribution function of an indefinite quadratic form. Some of these distribution functions, particularly the doubly noncentral cases, have traditionally involved fairly complicated expressions. The form presented in this paper is computationally straightforward and is attractive because it presents these related distributions as special cases of a single equation.

Keywords:

• Distribution functions
• chi-square
• f
• beta
• quadratic forms
• noncentral