The Gaussian Distribution¶

gsl_ran_gaussian
(sigma)¶ This function returns a Gaussian random variate, with mean zero and standard deviation
sigma
. The probability distribution for Gaussian random variates is,\[p(x) dx = {1 \over \sqrt{2 \pi \sigma^2}} \exp (x^2 / 2\sigma^2) dx\]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 BoxMuller algorithm which requires two calls to the random number generator.

gsl_ran_gaussian_pdf
(x, sigma)¶ This function computes the probability density \(p(x)\) at \(x\) for a Gaussian distribution with standard deviation
sigma
, using the formula given above.

gsl_ran_gaussian_ziggurat
(sigma)¶

gsl_ran_gaussian_ratio_method
(sigma)¶ These functions compute a Gaussian random variate using the alternative MarsagliaTsang ziggurat and KindermanMonahanLeva ratio methods. The Ziggurat algorithm is the fastest available algorithm in most cases.

gsl_ran_ugaussian
()¶

gsl_ran_ugaussian_pdf
(x)¶

gsl_ran_ugaussian_ratio_method
()¶ These functions compute results for the unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of one,
sigma
= 1.

gsl_cdf_gaussian_P
(x, sigma)¶

gsl_cdf_gaussian_Q
(x, sigma)¶

gsl_cdf_gaussian_Pinv
(P, sigma)¶

gsl_cdf_gaussian_Qinv
(Q, sigma)¶ These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the Gaussian distribution with standard deviation
sigma
.

gsl_cdf_ugaussian_P
(x)¶

gsl_cdf_ugaussian_Q
(x)¶

gsl_cdf_ugaussian_Pinv
(P)¶

gsl_cdf_ugaussian_Qinv
(Q)¶ These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the unit Gaussian distribution.