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- Function:
*double***gsl_ran_gaussian***(const gsl_rng **`r`, double`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 Box-Muller algorithm which requires two calls to the random number generator`r`.

- Function:
*double***gsl_ran_gaussian_pdf***(double*`x`, double`sigma`) This function computes the probability density

*p(x)*at`x`for a Gaussian distribution with standard deviation`sigma`, using the formula given above.

- Function:
*double***gsl_ran_gaussian_ziggurat***(const gsl_rng **`r`, double`sigma`) - Function:
*double***gsl_ran_gaussian_ratio_method***(const gsl_rng **`r`, double`sigma`) -
This function computes 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.

- Function:
*double***gsl_ran_ugaussian***(const gsl_rng **`r`) - Function:
*double***gsl_ran_ugaussian_pdf***(double*`x`) - Function:
*double***gsl_ran_ugaussian_ratio_method***(const gsl_rng **`r`) These functions compute results for the unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of one,

`sigma`= 1.

- Function:
*double***gsl_cdf_gaussian_P***(double*`x`, double`sigma`) - Function:
*double***gsl_cdf_gaussian_Q***(double*`x`, double`sigma`) - Function:
*double***gsl_cdf_gaussian_Pinv***(double*`P`, double`sigma`) - Function:
*double***gsl_cdf_gaussian_Qinv***(double*`Q`, double`sigma`) These functions compute the cumulative distribution functions

*P(x)*,*Q(x)*and their inverses for the Gaussian distribution with standard deviation`sigma`.

- Function:
*double***gsl_cdf_ugaussian_P***(double*`x`) - Function:
*double***gsl_cdf_ugaussian_Q***(double*`x`) - Function:
*double***gsl_cdf_ugaussian_Pinv***(double*`P`) - Function:
*double***gsl_cdf_ugaussian_Qinv***(double*`Q`) These functions compute the cumulative distribution functions

*P(x)*,*Q(x)*and their inverses for the unit Gaussian distribution.