A Note on the Performance of the "Ahrens Algorithm"

Wolfgang Hörmann


This short note discusses performance bounds for "Ahrens" algorithm, that can generate random variates from continuous distributions with monotonically decreasing density. This rejection algorithms uses constant hat-functions and constant squeezes over many small intervals. The choice of these intervals is important. Ahrens has demonstrated that the equal area rule that uses strips of constant area leads to a very simple algorithm. We present bounds on the rejection constant of this algorithm depending only on the number of intervals.

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, universal generator, performance measures

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