Automatic random variate generation for simulation input

We develop and evaluate algorithms for generating random variates for simulation input. One group called automatic, or black-box algorithms can be used to sample from distributions with known density. They are based on the rejection principle. The hat function is generated automatically in a setup step using the idea of transformed density rejection. There, the density is transformed into a concave function and the minimum of several tangents is used to construct the hat function. The resulting algorithms are not too complicated and are quite fast. The principle is also applicable to random vectors. A second group of algorithms is presented that generate random variates directly from a given sample by implicitly estimating the unknown distribution. The best of these algorithms are based on the idea of naive resampling plus added noise. These algorithms can be interpreted as sampling from the kernel density estimates. This method can be also applied to random vectors. There, it can be interpreted as a mixture of naive resampling and sampling from the multi-normal distribution that has the same covariance matrix as the data. The algorithms described in the paper have been implemented in ANSI C in a library called UNURAN which is available via anonymous ftp.