×

Automating bivariate transformations. (English) Zbl 1465.62093

Summary: 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 A. G. Glen et al. [INFORMS J. Comput. 9, No. 3, 288–295 (1997; Zbl 0897.60022)]. 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).

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62-08 Computational methods for problems pertaining to statistics
60E05 Probability distributions: general theory
68W30 Symbolic computation and algebraic computation

Citations:

Zbl 0897.60022

Software:

APPL
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Glen A. G., Evans D. L., Leemis L. M.APPL: A probability programming language. Amer. Statistician (2001) 55(2):156-166CrossRef
[2] Glen A. G., Leemis L. M., Drew J. H.A generalized univariate change-of-variable transformation technique. INFORMS J. Comput. (1997) 9(3):288-295Link · Zbl 0897.60022
[3] Hogg R. V., McKean J. W., Craig A. T.Introduction to Mathematical Statistics (2005) 6th ed.(Prentice Hall, Upper Saddle River, NJ)
[4] Rose C., Smith M. D.Mathematical Statistics with Mathematica (2002) (Springer-Verlag, New York) · Zbl 0989.62001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.