Modification of a Nonparametric Procedure for Testing the Hypothesis About the Distributions of Random Variables

In order to improve the computational efficiency of testing the hypothesis about the distributions of random variables, the paper proposes a modified testing procedure. This procedure is based on determining the maximum estimation discrepancy for the distribution functions of the compared random variables, followed by the calculation and analysis of confidence intervals for the determined distribution function values. The hypothesis about the identity of distributions is confirmed if obtained confidence intervals overlap at a given level of significance. According to the results of computational experiments, the Kolmogorov–Smirnov and Pearson's chi-squared tests were compared using the following formulas for sampling the intervals of random variables: Sturgess’ rule, Heinhold–Gaede formula, and that of the modified method. Pairwise combinations of the following distributions of random variables are considered: uniform, normal, lognormal, and power- law. It is shown that the modified procedure can be generalized to the case of testing hypotheses about the distributions of multidimensional random variables. In contrast to Pearson's chi-squared test, the proposed modified procedure helps to bypass the problem associated with converting the range of random variables into multidimensional intervals.