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Непараметрические критерии согласия Колмогорова, Смирнова, омега-квадрат и ошибки при их применении

Непараметрические критерии согласия Колмогорова, Смирнова, омега-квадрат и ошибки при их применении

Abstract

In the article we have considered A. N. Kolmogorov and N. V. Smirnov papers dedicated to one-sided and two-sided goodness-of-fit and homogeneity tests. It has been shown that the term "Kolmogorov Smirnov test" used incorrectly. We have also given the recommendations on use of the terms "Kolmogorov test", "Smirnov test", "test of Kolmogorov-Smirnov type" and discussed omega-square test (Cramer-von Mises-Smirnov test). Typical errors in the application of these criterions have been considered, in particular to test for normality of the distribution of measurement results

Рассмотрены работы А.Н. Колмогорова и Н.В. Смирнова, посвященные односторонним и двухсторонним критериям согласия и однородности. Показано, что термин «критерий Колмогорова Смирнова» использовать некорректно. Даны рекомендации по использованию терминов «критерий Колмогорова», «критерий Смирнова», «критерий типа Колмогорова Смирнова». Обсуждается критерий омега-квадрат (Крамера Мизеса Смирнова). Рассмотрены типовые ошибки при применении перечисленных критериев, в частности, для проверки нормальности распределения результатов измерений

Keywords

МАТЕМАТИЧЕСКАЯ СТАТИСТИКА, КРИТЕРИИ СОГЛАСИЯ, КРИТЕРИЙ КОЛМОГОРОВА, КРИТЕРИИ СМИРНОВА, КРИТЕРИЙ ОМЕГА-КВАДРАТ, ПРЕДЕЛЬНЫЕ РАСПРЕДЕЛЕНИЯ, ОШИБКИ ПРИ АНАЛИЗЕ ДАННЫХ, ИСТОРИЯ СТАТИСТИКИ

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    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
gold