Ranking of normality tests
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2022), pp. 45-59
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The paper proposes a new approach that allows a comparative analysis of the normality tests. Using a series of distributions that consistently converge to the normal law as alternative hypotheses allowed us to introduce an interval scale by which it is possible to determine not only which of the compared criteria is better, but also how much better.
Keywords: statistical hypotheses, normality tests.
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A. A. Skrynnikov. Ranking of normality tests. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2022), pp. 45-59. http://geodesic.mathdoc.fr/item/VTPMK_2022_2_a3/

[1] Vadzinskij R. N., Handbook of Probability Distributions, Nauka Publ., SPb., 2001, 295 pp. (in Russian)

[2] Venttsel E. S., Probability theory, Nauka Publ., Moscow, 1969, 576 pp. (in Russian)

[3] Statistical methods. Checking the deviation of the probability distribution from the normal distribution, Izd-vo standartov, Moscow, 2002, 30 pp. (in Russian)

[4] Kendall M., Styuart A., Statistical conclusions and connections, Nauka Publ., Moscow, 1973, 900 pp. (in Russian)

[5] Kobzar A. I., Applied mathematical statistics. For engineers and scientists, Fizmatlit Publ., Moscow, 2006, 816 pp. (in Russian)

[6] Lemeshko B. Yu., Criteria for checking the deviation of the distribution from the normal law. Application Guide, NGTU, Novosibirsk, 2014, 192 pp. (in Russian)

[7] Lemeshko B. Yu., Lemeshko S. B., “Sravnitelnyj analiz kriteriev proverki otkloneniya raspredeleniya ot normalnogo zakona”, Metrology, 2005, no. 2, 3–23 (in Russian)

[8] Lemeshko B. Yu., Rogozhnikov A. P., “Issledovanie osobennostej i moshchnosti nekotorykh kriteriev normalnosti”, Metrology, 2009, no. 4, 3–24 (in Russian) | MR

[9] Monsik V. B., Skrynnikov A. A., Probability theory and mathematical statistics. Statistical hypothesis testing, MGTU GA, Moscow, 2005, 64 pp. (in Russian)

[10] Anderson T. W., Darling D. A., “Asymptotic theory of certain “goodness-of-fit” criteria based on stochastic processes”, Annals of Mathematical Statistics, 23 (1952), 193–212 | DOI | MR | Zbl

[11] Arnastauskaite J., Ruzgas T., Brazenas M., “An exhaustive power comparison of normality tests”, Mathematics, 2021, no. 9, 788 | DOI

[12] BenSai da.A., Shapiro-Wilk and Shapiro-Francia normality tests, MATLAB Central File Exchange https://www.mathworks.com/matlabcentral/fileexchange/13964-shapiro-wilk-and-shapiro-francia-normality-tests

[13] Lilliefors H., “On the Kolmogorov–Smirnov test for normality with mean and variance unknown”, Journal of the American Statistical Association, 62:318 (1967), 399–402 | DOI

[14] Royston P., “An Extension of Shapiro and Wilk's W Test for Normality to Large Samples”, Journal of the Royal Statistical Society: Series C (Applied Statistics), 31:2 (1982a), 115–124 | Zbl

[15] Royston P., “Approximating the Shapiro-Wilk W-test for non-normality”, Statistics and Computing, 2 (1992), 117–119 | DOI

[16] Shapiro S. S., Wilk M. B., “An Analysis of Variance Test for Normality (Complete Samples)”, Biometrika, 52:3/4 (1965), 591–611 | DOI | MR | Zbl

[17] Shapiro S. S., Wilk M. B., Chen H. J., “A Comparative Study of Various Tests for Normality”, Journal of the American Statistical Association, 63:324 (1968), 1343–1372 | DOI | MR

[18] Thode H. C., Testing For Normality, CRC Press, Boca Raton, 2002, 368 pp.