The acceptance-complement method revisited

2026/07/23 by Luc Devroye · 1 voice
#stat.CO

paper · pdf

Abstract

We revisit the acceptance-complement method in random variate generation and show how it can replace the rejection method in many examples. While the rejection method has geometrically distributed execution times, the acceptance-complement method has a constant (deterministic) run time and qualifies as a ``one-liner''. We show how this method can be used to efficiently generate random variates from several distributions, such as the gamma and beta. In addition, we show that there is an acceptance-complement method that is valid for all log-concave densities with known location of the mode and black-box type access to the density.

Citations

• Polar Generation of Random Variates with the t-Distribution

Discussions

• Luc Devroye: The acceptance-complement method revisited https://arxiv.org/abs/2607.21275 https://arxiv.org/pdf/2607.21275 https://arxiv.org/html/2607.21275 [bsky, 0 points, 0 comments]

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