On a test for goodness-of-fit based on the empirical probability measure of Foutz and testing for exponentiality

Abstract

Foutz (1979) proposed a goodness-of-fit test for the simple hypothesis specifying a continuous p-variate distribution . For a suitably defined empirical probability measure, , the proposed test is based on the supremum of the absolute differences between hypothesized and empirical probabilities, the supremum being taken over all possible events. He showed that his test statistic was distribution free in the general p-variate case and derived its asymptotic null distribution. Here an alternate quick way of deriving the latter is proposed and connections are made to testing for exponentiality.

This research was supported by a Canada Council Killam Senior Research Fellowship and by a Natural Sciences and Engineering Research Council Canada Operating Grant, both held at Carleton University, Ottawa.