Parameterized Kolmogorov-Smirnov Test for Normality

The first (main) aim of the article is to define and practically apply the parameterized Kolmogorov-Smirnov goodness-of-fit test for normality. These modifications consist in varying a formula for calculating the empirical distribution function (EDF). The second contribution is to expand the EDF family with four new proposals. The third contribution is to create a family of alternative distributions, consisting of both older and newer distributions that, thanks to their flexibility, belong to all groups of skewness and kurtosis signs. Critical values are obtained using 106 order statistics for sample sizes n = 10, 20 and at a significance level a = 0.05. The fourth contribution is to calculate the power of the analyzed tests for alternative distributions based on 105 values of test statistics, with parameters selected so that they are similar to the normal distribution in various ways. The effectiveness of the analyzed tests is illustrated by analyzing real datasets.