An algorithm for fast generation of bivariate Poisson random vectors

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.