Inverse Gaussian Distribution - Generating Random Variates From An 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).

If

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; }

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