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Efficient calculation of the joint distribution of order statistics

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  • von Schroeder, Jonathan
  • Dickhaus, Thorsten

Abstract

The problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models is considered. While recursive formulae for evaluating the joint cumulative distribution function of such order statistics exist, their numerical implementation remains a challenging task. This task is tackled by presenting novel generalizations of known recursions. They are utilized to obtain exact results (calculated in rational arithmetic) as well as faithfully rounded results. Finally, some applications in goodness-of-fit testing, step-wise multiple hypothesis testing, and sample size calculation for studies with multiple endpoints are discussed.

Suggested Citation

  • von Schroeder, Jonathan & Dickhaus, Thorsten, 2020. "Efficient calculation of the joint distribution of order statistics," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:csdana:v:144:y:2020:i:c:s0167947319302543
    DOI: 10.1016/j.csda.2019.106899
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    References listed on IDEAS

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    1. Ferreira José António & Zwinderman Aeilko H, 2006. "Approximate Power and Sample Size Calculations with the Benjamini-Hochberg Method," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-38, September.
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    4. Helmut Finner & Veronika Gontscharuk & Thorsten Dickhaus, 2012. "False Discovery Rate Control of Step-Up-Down Tests with Special Emphasis on the Asymptotically Optimal Rejection Curve," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 382-397, June.
    5. Moscovich, Amit & Nadler, Boaz, 2017. "Fast calculation of boundary crossing probabilities for Poisson processes," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 177-182.
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