Based on the substitution principle, we derive one-sample goodness-of-fit tests of Kolmogorov-Smirnov and Cramér-von Mises type, respectively. In the case of a completely specified null hypothesis, these tests are distribution-free, if the cumulative distribution function under the null is a continuous function. In the case of composite null hypotheses, we consider location-scale families, along with the maximum likelihood estimators of their parameters. In such cases, tests of Kolmogorov-Smirnov and Cramér-von Mises type are parameter-free and can be calibrated by means of computer simulations under an arbitrary distribution belonging to the null hypothesis.
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