Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Numerical Methods for Fitting and Simulating Autoregressive-To-Anything Processes
INFORMS Journal on Computing
Initialization for NORTA: Generation of Random Vectors with Specified Marginals and Correlations
INFORMS Journal on Computing
Behavior of the NORTA method for correlated random vector generation as the dimension increases
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Numerical computation of rectangular bivariate and trivariate normal and t probabilities
Statistics and Computing
A method for fast generation of bivariate Poisson random vectors
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
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We present the “trivariate reduction extension” (TREx)---an exact algorithm for the fast generation of bivariate Poisson random vectors. Like the normal-to-anything (NORTA) procedure, TREx has two phases: a preprocessing phase when the required algorithm parameters are identified, and a generation phase when the parameters identified during the preprocessing phase are used to generate the desired Poisson vector. We prove that the proposed algorithm covers the entire range of theoretically feasible correlations, and we provide efficient-computation directives and rigorous bounds for truncation error control. We demonstrate through extensive numerical tests that TREx, being a specialized algorithm for Poisson vectors, has a preprocessing phase that is uniformly a hundred to a thousand times faster than a fast implementation of NORTA. The generation phases of TREx and NORTA are comparable in speed, with that of TREx being marginally faster. All code is publicly available.