Abstract
This chapter extends the work in the previous chapter in order to automate the bivariate change-of-variables technique for bivariate continuous random variables with arbitrary distributions. The algorithm from the previous chapter for univariate change-of-variables was originally devised by Glen et al. [37]. The bivariate transformation procedure presented in this chapter handles 1-to-1, k-to-1, and piecewise k-to-1 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).
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References
Glen AG, Drew JH, Leemis LM (1997) A generalized univariate change-of-variable transformation technique. INFORMS J Comput 9:288–295
Hogg RV, McKean JW, Craig AT (2005) Introduction to the mathematical statistics, 6th edn. Prentice-Hall, Upper Saddle River, New Jersey
Rose C, Smith MD (2002) Mathematical statistics and mathematica. Springer, New York
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Drew, J.H., Evans, D.L., Glen, A.G., Leemis, L.M. (2017). Bivariate 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_5
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DOI: https://doi.org/10.1007/978-3-319-43323-3_5
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