Analysis and comparison of some criteria of checking the probability distribution deviation from the normal distribution law

L. N. Aleksandrovskaya (), P. A. Iosifov and A. V. Kirillin
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L. N. Aleksandrovskaya: Moscow Aviation Institute (National Research University)
P. A. Iosifov: Moscow Aviation Institute (National Research University)
A. V. Kirillin: Moscow Aviation Institute (National Research University)

International Journal of System Assurance Engineering and Management, 2019, vol. 10, issue 1, No 3, 12-20

Abstract: Abstract A number of criteria of sample data concordance with the normal probability distribution law has been classified, and some recommendations for using these criteria in practice of engineering statistical analysis have been given. An original approach to testing the considered criteria has been proposed, which is based on the logics of building significance criteria, which allowed placlacing the criteria in the order of preference, when the standard normal distribution is taken for reference. This approach has been tested earlier in assessing adequacy of statistical mathematical models and assessing the degree of statistical similarity, when the information about performance quality of complex technical systems is combined, which was obtained in the process of experimental development. However, applying this approach to the problems of comparing criteria of measurement data concordance with the normal probabilities distribution law required additional research caused by lack of programs and tables of percentage points normality criteria statistics. The article presents the results of using of the interval estimation and experimental-statistical method of Taguchi for solving the problem.

Keywords: Checking deviations from the normal probability distribution law; Significance criteria; Significance levels; Geary criterion; Romanovsky; Shapiro–Wilk; Shapiro-Francia; Spiegelhalter; David-Hartley-Pearson; Epps-Pally; Hegazy-Green; Frosini; Sarkadi; The Taguchi loss function (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13198-019-00761-5

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