— Function: double gsl_ran_gumbel1 (const gsl_rng * r, double a, double b)

This function returns a random variate from the Type-1 Gumbel distribution. The Type-1 Gumbel distribution function is,

          p(x) dx = a b \exp(-(b \exp(-ax) + ax)) dx

for -\infty < x < \infty.

— Function: double gsl_ran_gumbel1_pdf (double x, double a, double b)

This function computes the probability density p(x) at x for a Type-1 Gumbel distribution with parameters a and b, using the formula given above.

— Function: double gsl_cdf_gumbel1_P (double x, double a, double b)
— Function: double gsl_cdf_gumbel1_Q (double x, double a, double b)
— Function: double gsl_cdf_gumbel1_Pinv (double P, double a, double b)
— Function: double gsl_cdf_gumbel1_Qinv (double Q, double a, double b)

These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Type-1 Gumbel distribution with parameters a and b.