A simple generalization of the Box-Muller method for obtaining a pair of correlated standard normal variables

In the simple and widely used method of Box-Muller [G. Box and M. Muller, A note on the generation of random normal deviates, Ann. Math. Statist. 29 (1958), pp. 610-611], from a pair of uniform and independent random variables in (0,1), a pair of standard and independent normal variables is obtained...

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Bibliographic Details
Published in:Journal of statistical computation and simulation 2010-09, Vol.80 (9), p.953-958
Main Author: Dias, J. Rodrigues
Format: Article
Language:English
Subjects:
bivariate normal vector
Box-Muller method
Coefficients
Computation
Computer simulation
Correlation
Correlation analysis
generalization
Mathematical analysis
Mathematical models
Random variables
Simulation
Statistical analysis
Statistical methods
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Summary:In the simple and widely used method of Box-Muller [G. Box and M. Muller, A note on the generation of random normal deviates, Ann. Math. Statist. 29 (1958), pp. 610-611], from a pair of uniform and independent random variables in (0,1), a pair of standard and independent normal variables is obtained. In this article, we present a very simple and elegant generalization of this method to obtain a pair of correlated standard normal variables with a given coefficient of correlation. This generalized method, which is computationally very easy, is interpreted in geometric terms, considering a translation of the uniform interval (0,1) and a rotation of a defined angle, both related to the coefficient of correlation. Some numerical results are simulated and statistically analysed, proving that the generalization is extremely simple and powerful.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949650902839162