Theoretical Basis
The underlying theory may be summarized as follows:
If u is uniformly distributed in the interval 0 ≤ u < 1, then the point (cos(2πu), sin(2πu)) is uniformly distributed on the unit circumference x2 + y2 = 1, and multiplying that point by an independent random variable ρ whose distribution is
will produce a point
whose coordinates are jointly distributed as two independent standard normal random variables.
Read more about this topic: Marsaglia Polar Method
Famous quotes containing the words theoretical and/or basis:
“The hypothesis I wish to advance is that ... the language of morality is in ... grave disorder.... What we possess, if this is true, are the fragments of a conceptual scheme, parts of which now lack those contexts from which their significance derived. We possess indeed simulacra of morality, we continue to use many of the key expressions. But we have—very largely if not entirely—lost our comprehension, both theoretical and practical, of morality.”
—Alasdair Chalmers MacIntyre (b. 1929)
“Even upon such a basis hast thou built
A monument, whose cement hath been guilt!”
—George Gordon Noel Byron (1788–1824)