Comparative analysis of the power of goodness-of-fit tests for composite hypotheses in dependence on the estimation method

The results are presented of the power comparison of the Kolmogorov, Cramer–von Mises–Smirnov and Anderson–Darling goodness-of-fit tests for composite hypotheses, depending on the method of parameter estimation. They demonstrate that the maximal power of the tests is achieved by using the maximum likelihood estimation method has the maximal power of tests inn estimating the scale parameter and evaluating both parameters of the normal distribution law. The power is higher at $L$-estimates in the case of the shape parameter of the Weibull distribution law. In estimating the shift parameter, the maximum power is observed in the case of the minimal distance method minimizing the relevant test statistic.