Marsaglia Polar Method - History

History

This idea dates back to Laplace, whom Gauss credits with finding the above

by taking the square root of

I^2 = \int_{-\infty}^\infty\int_{-\infty}^\infty e^{-(x^2+y^2)/2}\,dx\,dy =\int_0^{2\pi}\int_0^\infty re^{-r^2/2} \, dr \, d\theta.

The transformation to polar coordinates makes evident that θ is uniformly distributed (constant density) from 0 to 2π, and that the radial distance r has density

(Note that r2 has the appropriate chi square distribution.)

This method of producing a pair of independent standard normal variates by radially projecting a random point on the unit circumference to a distance given by the square root of a chi-square-2 variate is called the polar method for generating a pair of normal random variables,

Read more about this topic:  Marsaglia Polar Method

Famous quotes containing the word history:

    “All history is a record of the power of minorities, and of minorities of one.”
    —Ralph Waldo Emerson (1803–1882)

    “The history of all previous societies has been the history of class struggles.”
    —Karl Marx (1818–1883)

    “Don’t you realize that this is a new empire? Why, folks, there’s never been anything like this since creation. Creation, huh, that took six days, this was done in one. History made in an hour. Why it’s a miracle out of the Old Testament!”
    —Howard Estabrook (1884–1978)