The Distribution of Order Statistics for Discrete Random Variables with Applications to Bootstrapping

Authors:
Diane L. Evans;Lawrence M. Leemis;John H. Drew
Affiliations:
Department of Mathematics, RoseHulman Institute of Technology, 5500 Wabash Avenue, Terre Haute, Indiana 47803, USA;Department of Mathematics, The College of William & Mary, P.O. Box 8795, Williamsburg, Virginia 231878795, USA;Department of Mathematics, The College of William & Mary, P.O. Box 8795, Williamsburg, Virginia 231878795, USA
Venue:
INFORMS Journal on Computing
Year:
2006

Citing 2
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Abstract

An algorithm for computing the PDF of order statistics drawn from discrete parent populations is presented, along with an implementation of the algorithm in a computer algebra system. Several examples and applications, including exact bootstrapping analysis, illustrate the utility of this algorithm. Bootstrapping procedures require that B bootstrap samples be generated in order to perform statistical inference concerning a data set. Although the requirements for the magnitude of B are typically modest, a practitioner would prefer to avoid the resampling error introduced by choosing a finite B, if possible. The part of the order-statistic algorithm for sampling with replacement from a finite sample can be used to perform exact bootstrapping analysis in certain applications, eliminating the need for replication in the analysis of a data set.