Fast Generation of Order Statistics

Hörmann, Wolfgang and Derflinger, Gerhard (2001) Fast Generation of Order Statistics. Preprint Series / Department of Applied Statistics and Data Processing, 38. Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna.


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Generating a single order statistic without generating the full sample can be an important task for simulations. If the density and the CDF of the distribution are given it is no problem to compute the density of the order statistic. In the main theorem it is shown that the concavity properties of that density depend directly on the distribution itself. Especially for log-concave distributions all order statistics have log-concave distributions themselves. So recently suggested automatic transformed density rejection algorithms can be used to generate single order statistics. This idea leads to very fast generators. For example for the normal and gamma distribution the suggested new algorithms are between 10 and 60 times faster than the algorithms suggested in the literature. (author's abstract)

Item Type: Paper
Additional Information: published in: ACM Transactions on Modeling and Computer Simulation 12(2), pp. 83-93, 2002
Keywords: random variate generation / rejection method / transformed density rejection / order statistics / universal generator / T-concave
Classification Codes: MSC 65C10, CCS G.3
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 10 Jul 2006 11:28
Last Modified: 22 Oct 2019 00:41


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