IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i7p788-d530863.html
   My bibliography  Save this article

An Exhaustive Power Comparison of Normality Tests

Author

Listed:
  • Jurgita Arnastauskaitė

    (Department of Applied Mathematics, Kaunas University of Technology, 51368 Kaunas, Lithuania
    Department of Computer Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania)

  • Tomas Ruzgas

    (Department of Computer Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania)

  • Mindaugas Bražėnas

    (Department of Mathematical modelling, Kaunas University of Technology, 51368 Kaunas, Lithuania)

Abstract

A goodness-of-fit test is a frequently used modern statistics tool. However, it is still unclear what the most reliable approach is to check assumptions about data set normality. A particular data set (especially with a small number of observations) only partly describes the process, which leaves many options for the interpretation of its true distribution. As a consequence, many goodness-of-fit statistical tests have been developed, the power of which depends on particular circumstances (i.e., sample size, outlets, etc.). With the aim of developing a more universal goodness-of-fit test, we propose an approach based on an N-metric with our chosen kernel function. To compare the power of 40 normality tests, the goodness-of-fit hypothesis was tested for 15 data distributions with 6 different sample sizes. Based on exhaustive comparative research results, we recommend the use of our test for samples of size n ≥ 118 .

Suggested Citation

  • Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "An Exhaustive Power Comparison of Normality Tests," Mathematics, MDPI, vol. 9(7), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:788-:d:530863
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/7/788/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/7/788/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Jin & Wu, Yuehua, 2005. "Likelihood-ratio tests for normality," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 709-721, June.
    2. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    3. M. Mahibbur Rahman & Z. Govindarajulu, 1997. "A modification of the test of Shapiro and Wilk for normality," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(2), pages 219-236.
    4. Coin, Daniele, 2008. "A goodness-of-fit test for normality based on polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2185-2198, January.
    5. Gel, Yulia R. & Miao, Weiwen & Gastwirth, Joseph L., 2007. "Robust directed tests of normality against heavy-tailed alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2734-2746, February.
    6. Paul Zhang, 1999. "Omnibus test of normality using the Q statistic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 519-528.
    7. Bonett, Douglas G. & Seier, Edith, 2002. "A test of normality with high uniform power," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 435-445, September.
    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. Atif Avdović & Vesna Jevremović, 2022. "Quantile-Zone Based Approach to Normality Testing," Mathematics, MDPI, vol. 10(11), pages 1-16, May.

    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. repec:jss:jstsof:28:i03 is not listed on IDEAS
    2. Aldo Goia & Ernesto Salinelli & Pascal Sarda, 2015. "A new powerful version of the BUS test of normality," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 449-474, September.
    3. Charalampos Basdekis & Apostolos Christopoulos & Alexandros Gkolfinopoulos & Ioannis Katsampoxakis, 2022. "VaR as a risk management framework for the spot and futures tanker markets," Operational Research, Springer, vol. 22(4), pages 4287-4352, September.
    4. Coin, Daniele, 2008. "A goodness-of-fit test for normality based on polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2185-2198, January.
    5. Hui, Wallace & Gel, Yulia R. & Gastwirth, Joseph L., 2008. "lawstat: An R Package for Law, Public Policy and Biostatistics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i03).
    6. Gel, Yulia R. & Miao, Weiwen & Gastwirth, Joseph L., 2007. "Robust directed tests of normality against heavy-tailed alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2734-2746, February.
    7. Ardian Harri & Keith H. Coble, 2011. "Normality testing: two new tests using L-moments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1369-1379, May.
    8. Gel, Yulia R. & Gastwirth, Joseph L., 2008. "A robust modification of the Jarque-Bera test of normality," Economics Letters, Elsevier, vol. 99(1), pages 30-32, April.
    9. Luboš Střelec, 2008. "Comparison of power of modified Jarque-Bera normality tests and selected tests of normality [Srovnání síly modifikovaných Jarque-Bera testů a vybraných testů normality]," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 56(6), pages 137-148.
    10. Islam, Tanweer ul, 2008. "Normality Testing- A New Direction," MPRA Paper 16452, University Library of Munich, Germany.
    11. Havva Alizadeh Noughabi, 2016. "Two Powerful Tests for Normality," Annals of Data Science, Springer, vol. 3(2), pages 225-234, June.
    12. Bierens, H.J. & Broersma, L., 1991. "The relation between unemployment and interest rate : some international evidence," Serie Research Memoranda 0112, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    13. Juncal Cunado & David Gabauer & Rangan Gupta, 2024. "Realized volatility spillovers between energy and metal markets: a time-varying connectedness approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-17, December.
    14. Elie Bouri & Georges Azzi, 2014. "On the Dynamic Transmission of Mean and Volatility across the Arab Stock Markets," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 13(3), pages 279-304, December.
    15. Eric Fur, 2023. "Risk and return of classic car market prices: passion or financial investment?," Journal of Asset Management, Palgrave Macmillan, vol. 24(1), pages 59-68, February.
    16. Georgiev, Iliyan, 2010. "Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables," Journal of Econometrics, Elsevier, vol. 158(1), pages 37-50, September.
    17. Ericsson, Neil R., 2016. "Eliciting GDP forecasts from the FOMC’s minutes around the financial crisis," International Journal of Forecasting, Elsevier, vol. 32(2), pages 571-583.
    18. Jin, Xiaoye, 2015. "Volatility transmission and volatility impulse response functions among the Greater China stock markets," Journal of Asian Economics, Elsevier, vol. 39(C), pages 43-58.
    19. G. D. Gettinby & C. D. Sinclair & D. M. Power & R. A. Brown, 2004. "An Analysis of the Distribution of Extreme Share Returns in the UK from 1975 to 2000," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5‐6), pages 607-646, June.
    20. Damian Jelito & Marcin Pitera, 2018. "New fat-tail normality test based on conditional second moments with applications to finance," Papers 1811.05464, arXiv.org, revised Apr 2020.
    21. Ilham Haouas & Naceur Kheraief & Arusha Cooray & Syed Jawad Hussain Shahzad, 2019. "Time-Varying Casual Nexuses Between Remittances and Financial Development in Some MENA Countries," Working Papers 1294, Economic Research Forum, revised 2019.

    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:9:y:2021:i:7:p:788-:d:530863. 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.