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Modifi cation of a nonparametric method for testing the hypothesis of distributions of random variables
https://doi.org/10.32446/0368-1025it.2023-4-11-17
Abstract
To improve the computational effi ciency of solving the problem of testing the hypothesis about the distributions of random variables, a modifi ed testing technique is proposed. The technique is based on determining the maximum discrepancy between the estimates of the distribution functions of the compared random variables and further calculation and analysis of confi dence intervals for the found values of the distribution functions. The hypothesis about the identity of the distribution laws is confi rmed if the obtained confi dence intervals at a given level of signifi cance intersect. Based on the results of computational experiments, the Kolmogorov-Smirnov, Pearson criteria are compared using the formulas for sampling the intervals of values of random variables of Sturges, Heinhold-Gaede, and the modifi ed method. Paired combinations of random variable distribution laws are considered: uniform, Gaussian, lognormal and power law. Competence conditions for the compared criteria for testing hypotheses about the distributions of random variables are established. The modifi ed method allows its generalization to test the hypothesis of distributions of multidimensional random variables. In contrast to the Pearson criterion, the proposed technique allows to bypass the problem of decomposition of the range of values of random variables into multidimensional intervals.
About the Authors
A. V. Lapko
Institute of Computational Modelling of the Siberian Branch of the Russian Academy of Sciences; Institute of Computational Modelling of the Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Aleksandr V. Lapko
Krasnoyarsk
V. A. Lapko
Institute of Computational Modelling of the Siberian Branch of the Russian Academy of Sciences; Reshetnev Siberian State University of Science and Technology
Russian Federation
Russian Federation
Vasiliy A. Lapko
Krasnoyarsk
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Review
For citations:
Lapko A.V., Lapko V.A. Modifi cation of a nonparametric method for testing the hypothesis of distributions of random variables. Izmeritel`naya Tekhnika. 2023;(4):11-17. (In Russ.) https://doi.org/10.32446/0368-1025it.2023-4-11-17
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