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Quantile-Zone Based Approach to Normality Testing

Author

Listed:
  • Atif Avdović

    (Department of Natural Sciences and Mathematics, State University of Novi Pazar, 36300 Novi Pazar, Serbia)

  • Vesna Jevremović

    (Department of Natural Sciences and Mathematics, State University of Novi Pazar, 36300 Novi Pazar, Serbia)

Abstract

Normality testing remains an important issue for researchers, despite many solutions that have been published and in use for a long time. There is a need for testing normality in many areas of research and application, among them in Quality control, or more precisely, in the investigation of Shewhart-type control charts. We modified some of our previous results concerning control charts by using the empirical distribution function, proper choice of quantiles and a zone function that quantifies the discrepancy from a normal distribution. That was our approach in constructing a new normality test that we present in this paper. Our results show that our test is more powerful than any other known normality test, even in the case of alternatives with small departures from normality and for small sample sizes. Additionally, many test statistics are sensitive to outliers when testing normality, but that is not the case with our test statistic. We provide a detailed distribution of the test statistic for the presented test and comparable power analysis with highly illustrative graphics. The discussion covers both the cases for known and for estimated parameters.

Suggested Citation

  • Atif Avdović & Vesna Jevremović, 2022. "Quantile-Zone Based Approach to Normality Testing," Mathematics, MDPI, vol. 10(11), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1828-:d:824641
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    References listed on IDEAS

    as
    1. Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study," Mathematics, MDPI, vol. 9(23), pages 1-20, November.
    2. Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "An Exhaustive Power Comparison of Normality Tests," Mathematics, MDPI, vol. 9(7), pages 1-20, April.
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    Cited by:

    1. Raúl Alejandro Morán-Vásquez & Edwin Zarrazola & Daya K. Nagar, 2022. "Some Statistical Aspects of the Truncated Multivariate Skew- t Distribution," Mathematics, MDPI, vol. 10(15), pages 1-14, August.

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