--ZusammenfassungGenerating Beta Variates via Patchwork Rejection. A new algorithm for sampling from beta(p,q) distributions with parameters p > 1, q > 1 is developed. It is based on a method by Minh [9] which improves acceptance-rejection sampling in the main part of the distributions. Additionally, transformed uniform deviates can often be accepted immediately, so that much fewer than two uniforms are needed for one beta variate, on the average. The remaining tests for acceptance are enhanced by 'squeezes'. Experiments covering a wide range of pairs (p, q) showed improvements in speed over competing algorithms in most cases.

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 f͑x͒ 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 f͑x͒ 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.