On a test for goodness-of-fit based on the empirical probability measure of Foutz and testing for exponentiality
Foutz (1979) proposed a goodness-of-fit test for the simple hypothesis specifying a continuous p-variate distribution Open image in new window . For a suitably defined empirical probability measure, Open image in new window , 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.
KeywordsBrownian Bridge Quantile Process Equivalent Block Mise Type Borel Class
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