This function returns a Gaussian random variate, with mean zero and standard deviation sigma. The probability distribution for Gaussian random variates is,
for \(x\) in the range \(-\infty\) to \(+\infty\). Use the transformation \(z = \mu + x\) on the numbers returned by gsl_ran_gaussian to obtain a Gaussian distribution with mean \(\mu\). This function uses the Box-Muller algorithm which requires two calls to the random number generator.
This function computes the probability density \(p(x)\) at \(x\) for a Gaussian distribution with standard deviation sigma, using the formula given above.
These functions compute a Gaussian random variate using the alternative Marsaglia-Tsang ziggurat and Kinderman-Monahan-Leva ratio methods. The Ziggurat algorithm is the fastest available algorithm in most cases.
These functions compute results for the unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of one, sigma = 1.
These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the Gaussian distribution with standard deviation sigma.
These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the unit Gaussian distribution.