IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v6y2018i6p88-d149062.html
   My bibliography  Save this article

Computation of Probability Associated with Anderson–Darling Statistic

Author

Listed:
  • Lorentz Jäntschi

    (Department of Physics and Chemistry, Technical University of Cluj-Napoca, Muncii Blvd. No. 103-105, Cluj-Napoca 400641, Romania
    Doctoral Studies, Babeş-Bolyai University, Mihail Kogălniceanu Str., No. 1, Cluj-Napoca 400028, Romania)

  • Sorana D. Bolboacă

    (Department of Medical Informatics and Biostatistics, Iuliu Haţieganu University of Medicine and Pharmacy, Louis Pasteur Str., No. 6, Cluj-Napoca 400349, Romania)

Abstract

The correct application of a statistical test is directly connected with information related to the distribution of data. Anderson–Darling is one alternative used to test if the distribution of experimental data follows a theoretical distribution. The conclusion of the Anderson–Darling test is usually drawn by comparing the obtained statistic with the available critical value, which did not give any weight to the same size. This study aimed to provide a formula for calculation of p -value associated with the Anderson–Darling statistic considering the size of the sample. A Monte Carlo simulation study was conducted for sample sizes starting from 2 to 61, and based on the obtained results, a formula able to give reliable probabilities associated to the Anderson–Darling statistic is reported.

Suggested Citation

  • Lorentz Jäntschi & Sorana D. Bolboacă, 2018. "Computation of Probability Associated with Anderson–Darling Statistic," Mathematics, MDPI, vol. 6(6), pages 1-17, May.
  • Handle: RePEc:gam:jmathe:v:6:y:2018:i:6:p:88-:d:149062
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/6/6/88/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/6/6/88/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lafaye de Micheaux, Pierre & Tran, Viet Anh, 2016. "PoweR: A Reproducible Research Tool to Ease Monte Carlo Power Simulation Studies for Goodness-of-fit Tests in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i03).
    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. J. van Soest, 1967. "Some experimental results concerning tests of normality," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 21(1), pages 91-97, March.
    4. Havva Alizadeh Noughabi, 2016. "Two Powerful Tests for Normality," Annals of Data Science, Springer, vol. 3(2), pages 225-234, June.
    5. Bera, Anil K. & Jarque, Carlos M., 1981. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals : Monte Carlo Evidence," Economics Letters, Elsevier, vol. 7(4), pages 313-318.
    6. Rajen D. Shah & Peter Bühlmann, 2018. "Goodness‐of‐fit tests for high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 113-135, January.
    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. Huertas, José I. & Serrano-Guevara, Oscar & Díaz-Ramírez, Jenny & Prato, Daniel & Tabares, Lina, 2022. "Real vehicle fuel consumption in logistic corridors," Applied Energy, Elsevier, vol. 314(C).
    2. Lorentz Jäntschi, 2020. "Detecting Extreme Values with Order Statistics in Samples from Continuous Distributions," Mathematics, MDPI, vol. 8(2), pages 1-21, February.
    3. Robert Parham, 2023. "The Difference-of-Log-Normals Distribution: Properties, Estimation, and Growth," Papers 2302.02486, arXiv.org.

    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. Ladislav KRISTOUFEK & Petra LUNACKOVA, 2013. "Long-term Memory in Electricity Prices: Czech Market Evidence," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(5), pages 407-424, November.
    2. Lauren Bin Dong & David E. A. Giles, 2004. "An Empirical Likelihood Ratio Test for Normality," Econometrics Working Papers 0401, Department of Economics, University of Victoria.
    3. Giorgio Fagiolo & Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2010. "On the distributional properties of household consumption expenditures: the case of Italy," Empirical Economics, Springer, vol. 38(3), pages 717-741, June.
    4. Philip Arestis & Ana Rosa Gonzalez‐Martinez, 2019. "Economic precariousness: A new channel in the housing market cycle," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 24(2), pages 1030-1043, April.
    5. Alemayehu Geda & Atnafu Meskel, 2008. "China and India's Growth Surge: Is it a curse or blessing for Africa? The Case of Manufactured Exports," African Development Review, African Development Bank, vol. 20(2), pages 247-272.
    6. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    7. Kaul, Aditya & Kayacetin, Nuri Volkan, 2017. "Flight-to-quality, economic fundamentals, and stock returns," Journal of Banking & Finance, Elsevier, vol. 80(C), pages 162-175.
    8. Arvid Oskar Ivar Hoffmann & Wander Jager & J. H. Von Eije, 2007. "Social Simulation of Stock Markets: Taking It to the Next Level," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(2), pages 1-7.
    9. Mensah, Jones Odei & Premaratne, Gamini, 2018. "Dependence patterns among Asian banking sector stocks: A copula approach," Research in International Business and Finance, Elsevier, vol. 45(C), pages 357-388.
    10. Pavol Durana & Katarina Valaskova & Darina Chlebikova & Vladislav Krastev & Irina Atanasova, 2020. "Heads and Tails of Earnings Management: Quantitative Analysis in Emerging Countries," Risks, MDPI, vol. 8(2), pages 1-21, June.
    11. K. Lebedeva, 2015. "An Empirical Analysis of the Russian Financial Markets’ Liquidity and Returns," Review of Business and Economics Studies // Review of Business and Economics Studies, Финансовый Университет // Financial University, vol. 3(3), pages 5-31.
    12. Korbinian von Blanckenburg, Gerrit Reher, "undated". "Testverfahren zur Beurteilung der Funktionsfähigkeit von Marktprozessen," Working Papers 201154, Institute of Spatial and Housing Economics, Munster Universitary.
    13. M. Beatriz Mota Aragón & Faviola Hernández Jiménez, 2011. "Un modelo para evaluar el VPN mediante modelos autoregresivos," Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics), Tecnológico de Monterrey, Campus Ciudad de México, vol. 6(2), pages 66-87.
    14. Mr. Kenji Moriyama & Abdul Naseer, 2009. "Forecasting Inflation in Sudan," IMF Working Papers 2009/132, International Monetary Fund.
    15. Mezgebo, Taddese, 2009. "A multivariate approach for identification of optimal locations with in Ethiopia’s wheat market to tackle soaring inflation on food price," MPRA Paper 18663, University Library of Munich, Germany.
    16. Juliane Proelss & Denis Schweizer, 2014. "Polynomial goal programming and the implicit higher moment preferences of US institutional investors in hedge funds," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 28(1), pages 1-28, February.
    17. Kristoufek, Ladislav, 2009. "R/S analysis and DFA: finite sample properties and confidence intervals," MPRA Paper 16446, University Library of Munich, Germany.
    18. Kucherov, Dmitry G. & Tsybova, Victoria S. & Yu. Lisovskaia, Antonina & Alkanova, Olga N., 2022. "Brand orientation, employer branding and internal branding: Do they effect on recruitment during the COVID-19 pandemic?," Journal of Business Research, Elsevier, vol. 151(C), pages 126-137.
    19. Wu, Zewen, 2024. "Are we in a bubble? Financial vulnerabilities in semiconductor, Web3, and genetic engineering markets," International Review of Economics & Finance, Elsevier, vol. 90(C), pages 32-44.
    20. Wang, Yizhi, 2022. "Volatility spillovers across NFTs news attention and financial markets," International Review of Financial Analysis, Elsevier, vol. 83(C).

    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:6:y:2018:i:6:p:88-:d:149062. 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.