Random Walk and Distributions of Rank Order Statistics

Csaki and Vincze [2], [3] and Jain [7] derived the distributions of certain rank order statistics by Gnedenko's technique [6] employing random walk with nonindependent steps. Dwass [4] developed an alternate technique based on simple random walk with independent steps and gave simple proofs for...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1972-09, Vol.23 (2), p.276-287
Main Authors: Aneja, K. G., Sen, Kanwar
Format: Article
Language:English
Subjects:
Equalization
Equivalence relation
Hierarchies
Mathematical functions
Mathematics
Random variables
Random walk
Statistics
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Summary:Csaki and Vincze [2], [3] and Jain [7] derived the distributions of certain rank order statistics by Gnedenko's technique [6] employing random walk with nonindependent steps. Dwass [4] developed an alternate technique based on simple random walk with independent steps and gave simple proofs for some new as well as known distributions. In this paper, we derive the joint distributions of various rank order statistics through the technique of Dwass and unify into one method the results of Chung and Feller [1], Csaki and Vincze [2], [3], Dwass [4] and Jain [7]. In addition, we derive some new distributions and establish certain new equivalence relations.
ISSN:0036-1399
1095-712X
DOI:10.1137/0123029