The noncentral chi-squared distribution with zero degrees of freedom and testing for uniformity

Abstract

Abstract : The noncentral chi-squared distribution with zero degrees of freedom is defined as a Poisson mixture of mass at zero together with chi-squared distributions that have even degrees of freedom. Their name is justified by the decomposition of the classical noncentral chi-squared distributions as the sum of a central chi-squared component having the full number of degrees of freedom and an independent noncentral chi-squared component having zero degrees of freedom. The basic properties of this one-parameter family of distributions are given, and they are shown to be useful in the computation of approximate critical values of a test for uniformity. (Author)