Abstract

While testing composite hypotheses when a scalar or vector parameter of the probability distribution is calculated using the same sample, nonparametric Kolmogorov, Kuiper, Cramer–von Mises–Smirnov, Watson and Anderson–Darling goodness-of-fit tests lose their distribution freedom. When testing composite hypotheses conditional distribution of the test statistic depends on several factors, even the specific values of the distribution shape parameters. An interactive method for investigating distributions of nonparametric goodness-of-fit tests statistics, that allows us apply criteria for testing any composite hypotheses using a variety of estimation methods, is implemented.

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