IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i11p1828-d824641.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/11/1828/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/11/1828/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "An Exhaustive Power Comparison of Normality Tests," Mathematics, MDPI, vol. 9(7), pages 1-20, April.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nour Mohamad Fayad, 2024. "The Causality Between Corruption and Economic Growth in MENA Countries: A Dynamic Panel-Data Analysis," International Journal of Finance, Insurance and Risk Management, International Journal of Finance, Insurance and Risk Management, vol. 14(1), pages 28-49.
    2. Reza Sanei & Farhad Hosseinzadeh lotfi & Mohammad Fallah & Farzad Movahedi Sobhani, 2022. "An Estimation of an Acceptable Efficiency Frontier Having an Optimum Resource Management Approach, with a Combination of the DEA-ANN-GA Technique (A Case Study of Branches of an Insurance Company)," Mathematics, MDPI, vol. 10(23), pages 1-21, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1828-:d:824641. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.