Inverse Gaussian Distribution - Generating Random Variates From An Inverse-Gaussian Distribution | Generating Random Variates Inverse-Gaussian Distribution

Generating Random Variates From An Inverse-Gaussian Distribution

The following algorithm may be used.

Generate a random variate from a normal distribution with a mean of 0 and 1 standard deviation

$\displaystyle \nu = N(0,1).$

Square the value

$\displaystyle y = \nu^2$

and use this relation

$x = \mu + \frac{\mu^2 y}{2\lambda} - \frac{\mu}{2\lambda}\sqrt{4\mu \lambda y + \mu^2 y^2}.$

Generate another random variate, this time sampled from a uniformed distribution between 0 and 1

$\displaystyle z = U(0,1).$

$z \le \frac{\mu}{\mu+x}$

then return

$\displaystyle x$

else return

$\frac{\mu^2}{x}.$

Sample code in Java:

public double inverseGaussian(double mu, double lambda) { Random rand = new Random; double v = rand.nextGaussian; // sample from a normal distribution with a mean of 0 and 1 standard deviation double y = v*v; double x = mu + (mu*mu*y)/(2*lambda) - (mu/(2*lambda)) * Math.sqrt(4*mu*lambda*y + mu*mu*y*y); double test = rand.nextDouble; // sample from a uniform distribution between 0 and 1 if (test <= (mu)/(mu + x)) return x; else return (mu*mu)/x; }

Read more about this topic: Inverse Gaussian Distribution

Famous quotes containing the words random and/or distribution:

“There is a potential 4-6 percentage point net gain for the President [George Bush] by replacing Dan Quayle on the ticket with someone of neutral stature.”
—Mary Matalin, U.S. Republican political advisor, author, and James Carville b. 1946, U.S. Democratic political advisor, author. All’s Fair: Love, War, and Running for President, p. 205, Random House (1994)

“There is the illusion of time, which is very deep; who has disposed of it? Mor come to the conviction that what seems the succession of thought is only the distribution of wholes into causal series.”
—Ralph Waldo Emerson (1803–1882)