Evans, Diane L.; Leemis, Lawrence M.; Drew, John H. The distribution of order statistics for discrete random variables with applications to bootstrapping. (English) Zbl 1241.62076 INFORMS J. Comput. 18, No. 1, 19-30 (2006). Summary: 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. Cited in 3 Documents MSC: 62G30 Order statistics; empirical distribution functions 62E15 Exact distribution theory in statistics 68W30 Symbolic computation and algebraic computation 65C60 Computational problems in statistics (MSC2010) Keywords:combinatorial algorithm; computer algebra systems Software:APPL PDFBibTeX XMLCite \textit{D. L. Evans} et al., INFORMS J. Comput. 18, No. 1, 19--30 (2006; Zbl 1241.62076) Full Text: DOI