Abstract
This chapter presents a generalized version of the univariate change-of-variable technique for transforming continuous random variables. Extending a theorem from Casella and Berger [16] 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 APPL and present four examples.
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Drew, J.H., Evans, D.L., Glen, A.G., Leemis, L.M. (2017). Transformations of Random Variables. In: Computational Probability. International Series in Operations Research & Management Science, vol 246. Springer, Cham. https://doi.org/10.1007/978-3-319-43323-3_4
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DOI: https://doi.org/10.1007/978-3-319-43323-3_4
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