Fast Generation of Order Statistics

Wolfgang Hörmann and Gerhard Derflinger


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.

Mathematics Subject Classification: 65C10 (Random Number Generation)

CR Categories and Subject Descriptors: G.3 [Probability and Statistics]: Random number generation

General Terms: Algorithms

Key Words: random variate generation, rejection method, transformed density rejection, order statistics, universal generator, T-concave

Download Preprint
© ACM, (2002). This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Trans. Model. Comput. Simul. 12(2), 83-93 http://doi.acm.org/10.1145/566392.566393