Smoothed Transformed Density Rejection

Josef Leydold and Wolfgang Hörmann


There are situations in the framework of quasi-Monte Carlo integration where nonuniform low-discrepancy sequences are required. Using the inversion method for this task usually results in the best performance in terms of the integration errors. However, this method requires a fast algorithm for evaluating the inverse of the cumulative distribution function which is often not available. Then a smoothed version of transformed density rejection is a good alternative as it is a fast method and its speed hardly depends on the distribution. It can easily be adjusted such that it is almost as good as the inversion method. For importance sampling it is even better to use the hat distribution as importance distribution directly. Then the resulting algorithm is as good as using the inversion method for the original importance distribution but its generation time is much shorter.

Mathematics Subject Classification: 65C05 (Monte Carlo Methods) 65C10 (Random Number Generation) 65D30 (Numerical integration)

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

General Terms: Algorithms

Key Words: Monte Carlo method, quasi-Monte Carlo method, nonuniform random variate generation, transformed density rejection, smoothed rejection, inversion

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