Automating Bivariate Transformations

Abstract

We automate the bivariate change-of-variables technique for bivariate continuous random variables with arbitrary distributions. This extends the algorithm for univariate change-of-variables devised by Glen et al. [Glen, A. G., L. M. Leemis, J. H. Drew. 1997. A generalized univariate change-of-variable transformation technique. INFORMS J. Comput. 9(3) 288–295]. Our transformation procedure handles one–to–one, k–to–one, and piecewise k–to–one transformations for both independent and dependent random variables. We also present other procedures that operate on bivariate random variables (e.g., calculating correlation and marginal distributions).