The Patchwork Rejection Technique for Sampling from Unimodal Distributions

Abstract

We report on both theoretical developments and computational experience with the patchwork rejection technique in Zechner and Stadlober [1993] and Zechner [1997]. The basic approach is due to Minh [1988], who suggested a special sampling method for the gamma distribution. This method's general objective is to rearrange the area below the density or histogram f(x) in the body of the distribution by certain point reflections such that variates may be generated efficiently within a large center interval. This is carried out via uniform hat functions, combined with minorizing rectangles for immediate acceptance of one transformed uniform deviate. The remaining tails of f(x) are covered by exponential functions. Experiments show that patchwork rejection algorithms are in general faster than their competitors at the cost of higher set-up times.