A data based algorithm for the generation of random vectors
Computational Statistics & Data Analysis
Multivariate statistical simulation
Multivariate statistical simulation
A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Noninverse correlation induction: guidelines for algorithm development
Journal of Computational and Applied Mathematics - Random numbers and simulation
A rejection technique for sampling from T-concave distributions
ACM Transactions on Mathematical Software (TOMS)
Graphical interactive simulation input modeling with bivariate Bézier distributions
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on graphics, animation, and visualization for simulation environments
A rejection technique for sampling from log-concave multivariate distributions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Input modeling tools for complex problems
Proceedings of the 30th conference on Winter simulation
A sweep-plane algorithm for generating random tuples in simple polytopes
Mathematics of Computation
Automatic sampling with the ratio-of-uniforms method
ACM Transactions on Mathematical Software (TOMS)
Algorithm 802: an automatic generator for bivariate log-concave distributions
ACM Transactions on Mathematical Software (TOMS)
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Random dot product graph models for social networks
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
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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 co-variance matrix as the data. The algorithms described in this paper have been implemented in ANSI C in a library called UNURAN which is available via anonymous ftp.