W 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 pro...

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 is sampled using the popular NORmal-To-Anything procedure.) At the core of this method lies the question of sampling from a piecewise-linear connected region in the tail of a ...

The NORTA method is a fast general-purpose method for generating samples of a random vector with given marginal distributions and given correlation matrix. It is known that there exist marginal distributions and correlation matrices that the NORTA method cannot match, even though a random vector with the prescribed qualities exists. In this case we say that the correlation matrix is NORTA defec...

The NORmal-To-Anything (NORTA) algorithm requires a correlation matrix of multivariate normal variables to convert a multivariate normal vector to any other distribution. This paper presents a new simulation method that works in combination with the NORTA algorithm yet avoids having to solve some complicated equations which need to be solved to achieve this matrix. The performance of the propos...

We present “Trivariate Reduction Extension” (TREx) — an exact algorithm for fast generation of bivariate Poisson random vectors. Like the 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 t...

We describe a model for representing random vectors whose component random variables have arbitrary marginal distributions and correlation matrix, and describe how to generate data based upon this model for use in a stochastic simulation. The central idea is to transform a multivariate normal random vector into the desired random vector, so we refer to these vectors as having a NORTA (NORmal To...

The NORTA method for multivariate generation is a fast general purpose method for generating samples of a random vector with given marginal distributions and given productmoment or rank correlation matrix. However, this method has been shown to fail to work for some feasible correlation matrices. (A matrix is feasible if there exists a random vector with the given marginal distributions and the...

There is a growing need for the ability to specify and generate correlated random variables as primitive inputs to stochastic models. Motivated by this need, several authors have explored the generation of random vectors with specified marginals, together with a specified covariance matrix, through the use of a transformation of a multivariate normal random vector (the NORTA method). A covarian...