Computational & Applied Mathematics & Statistics
INFORMS Journal of Computing
We present a generalized version of the univariate change-of-variable technique for transforming continuous random variables. Extending a theorem from Casella and Berger [1990. Statistical Inference, Wadsworth and Brooks/Cole, Inc., Pacific Grove, CA] for many-to-1 transformations, we consider more general univariate transformations. Specifically, the transformation can range from 1-to-1 to many-to-1 on various subsets of the support of the random variable of interest. We also present an implementation of the theorem in a computer algebra system that automates the technique. Some examples demonstrate the theorem's application.
Glen, Andrew G.; Leemis, Lawrence; and Drew, John H., A Generalized Univariate Change-of-Variable Transformation Technique (1997). INFORMS Journal of Computing, 9(3), 231-318.
This version is the accepted (post-print) version of the manuscript.