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:

    “It may be well to remember that the highest level of moral aspiration recorded in history was reached by a few ancient Jews—Micah, Isaiah, and the rest—who took no count whatever of what might not happen to them after death. It is not obvious to me why the same point should not by and by be reached by the Gentiles.”
    —Thomas Henry Huxley (1825–95)

    “It takes a great deal of history to produce a little literature.”
    —Henry James (1843–1916)

    “Literary works cannot be taken over like factories, or literary forms of expression like industrial methods. Realist writing, of which history offers many widely varying examples, is likewise conditioned by the question of how, when and for what class it is made use of.”
    —Bertolt Brecht (1898–1956)