The Distribution of Order Statistics for Discrete Random Variables with Applications to Bootstrapping
Diane L. Evans, Lawrence M. Leemis, John H. Drew
INFORMS Journal on Computing · 2006 · Volume 18 · Issue 1
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.
Keywords
combinatorial algorithms, computer algebra systems, probability, probability distributions, statistics
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