A Generalized Univariate Change-of-Variable Transformation Technique
Andrew G. Glen, Lawrence M. Leemis, John H. Drew
INFORMS Journal on Computing · 1997 · Volume 9 · Issue 3
Abstract
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.
Keywords
probability, change-of-variable technique, distributions of functions of random variables
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