Parameterized Kolmogorov–Smirnov Test for Normality

The first (main) aim of the article is to define and practically apply the parameterized Kolmogorov–Smirnov (PKS) goodness-of-fit test for normality. The second contribution is to expand the family of empirical distribution functions with four new proposals. The third contribution is to construct a family of alternative distributions that includes both older and newer distributions. The fourth contribution is to calculate the power of the analyzed tests under alternative distributions with parameters chosen to be similar to the normal distribution in various ways. The new proposal is distinguished for left-skewed alternative distributions and symmetric distributions characterizing by negative excess kurtosis. The effectiveness of the PKS test is also illustrated by the analysis of thirty real data sets.