Efficient calculation of the joint distribution of order statistics

Jonathan von Schroeder and Thorsten Dickhaus

Computational Statistics & Data Analysis, 2020, vol. 144, issue C

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.

Keywords: Bolshev’s recursion; Faithful rounding; Noe’s recursion; Sample size planning; Steck’s recursion (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:144:y:2020:i:c:s0167947319302543

DOI: 10.1016/j.csda.2019.106899

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