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Computation of Probability Associated with Anderson–Darling Statistic

Author

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  • 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
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    References listed on IDEAS

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    Cited by:

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    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.

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