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Evaluating the Anderson-Darling Distribution

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  • Marsaglia, George
  • Marsaglia, John

Abstract

Except for n = 1, only the limit as n approaches infinity for the distribution of the Anderson-Darling test for uniformity has been found, and that in so complicated a form that published values for a few percentiles had to be determined by numerical integration, saddlepoint or other approximation methods. We give here our method for evaluating that asymptotic distribution to great accuracy--directly, via series with two-term recursions. We also give, for any particular n, a procedure for evaluating the distribution to the fourth digit, based on empirical CDF's from samples of size 1010 .

Suggested Citation

  • Marsaglia, George & Marsaglia, John, 2004. "Evaluating the Anderson-Darling Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i02).
    • Handle: RePEc:jss:jstsof:v:009:i02
    DOI: http://hdl.handle.net/10.18637/jss.v009.i02
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    2. Sung Ik Kim, 2022. "ARMA–GARCH model with fractional generalized hyperbolic innovations," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-25, December.
    3. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    4. Kristian Hindberg & Jan Hannig & Fred Godtliebsen, 2019. "A novel scale-space approach for multinormality testing and the k-sample problem in the high dimension low sample size scenario," PLOS ONE, Public Library of Science, vol. 14(1), pages 1-20, January.
    5. Shibin Zhang & Xin M. Tu, 2022. "Tests for comparing time‐invariant and time‐varying spectra based on the Anderson–Darling statistic," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(3), pages 254-282, August.
    6. Daniele Coin, 2017. "A goodness-of-fit test for Generalized Error Distribution," Temi di discussione (Economic working papers) 1096, Bank of Italy, Economic Research and International Relations Area.
    7. Konstantinos Leptokaropoulos & Catherine A. Rychert & Nicholas Harmon & David Schlaphorst & Ingo Grevemeyer & John-Michael Kendall & Satish C. Singh, 2023. "Broad fault zones enable deep fluid transport and limit earthquake magnitudes," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    8. Fernández de Marcos Giménez de los Galanes, Alberto & García Portugués, Eduardo, 2022. "Data-driven stabilizations of goodness-of-fit tests," DES - Working Papers. Statistics and Econometrics. WS 35324, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Asmerilda Hitaj & Lorenzo Mercuri & Edit Rroji, 2019. "Sensitivity analysis of Mixed Tempered Stable parameters with implications in portfolio optimization," Computational Management Science, Springer, vol. 16(1), pages 71-95, February.
    10. Kim, Young Shin & Lee, Jaesung & Mittnik, Stefan & Park, Jiho, 2015. "Quanto option pricing in the presence of fat tails and asymmetric dependence," Journal of Econometrics, Elsevier, vol. 187(2), pages 512-520.
    11. Grundke, Peter, 2010. "Top-down approaches for integrated risk management: How accurate are they?," European Journal of Operational Research, Elsevier, vol. 203(3), pages 662-672, June.
    12. Fernández-de-Marcos, Alberto & García-Portugués, Eduardo, 2023. "Data-driven stabilizations of goodness-of-fit tests," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    13. Andrey Feuerverger, 2016. "On Goodness of Fit for Operational Risk," International Statistical Review, International Statistical Institute, vol. 84(3), pages 434-455, December.
    14. Hasan A. Fallahgoul & Young S. Kim & Frank J. Fabozzi & Jiho Park, 2019. "Quanto Option Pricing with Lévy Models," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1279-1308, March.
    15. Gomes-Gonçalves, Erika & Gzyl, Henryk & Mayoral, Silvia, 2015. "Two maxentropic approaches to determine the probability density of compound risk losses," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 42-53.
    16. Zinoviy Landsman & Udi Makov & Tomer Shushi, 2017. "Extended Generalized Skew-Elliptical Distributions and their Moments," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-100, February.
    17. Grace, Adam W. & Wood, Ian A., 2012. "Approximating the tail of the Anderson–Darling distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4301-4311.
    18. Dobric, Jadran & Schmid, Friedrich, 2007. "A goodness of fit test for copulas based on Rosenblatt's transformation," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4633-4642, May.

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