An Efficient Method for Generating Discrete Random Variables with General Distributions
ACM Transactions on Mathematical Software (TOMS)
Simulation Modeling and Analysis
Simulation Modeling and Analysis
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)
Variance Reduction Techniques for Estimating Value-at-Risk
Management Science
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We propose C-NORTA, an exact algorithm to generate random variates from the tail of a bivariate NORTA random vector. (A NORTA random vector is specified by a pair of marginals and a rank or product--moment correlation, and it is sampled using the popular NORmal-To-Anything procedure.) We first demonstrate that a rejection-based adaptation of NORTA on such constrained random vector generation problems may often be fundamentally intractable. We then develop the C-NORTA algorithm, relying on strategic conditioning of the NORTA vector, followed by efficient approximation and acceptance/rejection steps. We show that, in a certain precise asymptotic sense, the sampling efficiency of C-NORTA is exponentially larger than what is achievable through a naïve application of NORTA. Furthermore, for at least a certain class of problems, we show that the acceptance probability within C-NORTA decays only linearly with respect to a defined rarity parameter. The corresponding decay rate achievable through a naïve adaptation of NORTA is exponential. We provide directives for efficient implementation.