SOLVING PROBLEMS OF USING SOME NONPARAMETRIC GOODNESS-OF-FIT TESTS
B. Yu. Lemeshko, A. A. Gorbunova, S. B. Lemeshko, A. P. Rogozhnikov
Novosibirsk State Technical University, pr. Karla Marksa 20, Novosibirsk, 630073 Russia
Keywords: nonparametric goodness-of-fit tests, Kuiper test, Watson test, Zhang tests, test power, simple and composite hypotheses
Abstract
Estimates are given of the power of the Kuiper and Watson goodness-of-fit tests and three Zhang tests with the ZA, ZC, and ZK statistics with respect to some pairs of competing laws in testing simple and composite hypotheses. The powers of these tests are compared with the powers of the Kolmogorov, Cramer-von Mises-Smirnov, and Anderson-Darling tests. Statistic distribution models and tables of percentage points are constructed which allow the Kuiper and Watson goodness-of-fit tests to be used to test composite hypotheses about the goodness of fit of samples against various parametric distribution laws. An interactive simulation method is proposed that allows constructing and using distributions of test statistics in solving problems of statistical analysis.
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