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Box-Muller Transformation

المؤلف:  Box, G. E. P. and Muller, M. E.

المصدر:  "A Note on the Generation of Random Normal Deviates." Ann. Math. Stat. 29

الجزء والصفحة:  ...

17-3-2021

1952

Box-Muller Transformation

A transformation which transforms from a two-dimensional continuous uniform distribution to a two-dimensional bivariate normal distribution (or complex normal distribution). If  and  are uniformly and independently distributed between 0 and 1, then  and  as defined below have a normal distribution with mean  and variance .

			(1)
			(2)

This can be verified by solving for  and ,

			(3)
			(4)

Taking the Jacobian yields

			(5)
			(6)

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REFERENCES:

Box, G. E. P. and Muller, M. E. "A Note on the Generation of Random Normal Deviates." Ann. Math. Stat. 29, 610-611, 1958.