### 20.27 The Type-2 Gumbel Distribution

Function: double gsl_ran_gumbel2 (const gsl_rng * r, double a, double b)

  This function returns a random variate from the Type-2 Gumbel distribution. The Type-2 Gumbel distribution function is,

      p(x) dx = a b x^{-a-1} \exp(-b x^{-a}) dx

  for 0 < x < \infty.

Function: double gsl_ran_gumbel2_pdf (double x, double a, double b)

  This function computes the probability density p(x) at x for a Type-2 Gumbel distribution with parameters a and b, using the formula given above.

Function: double gsl_cdf_gumbel2_P (double x, double a, double b)
Function: double gsl_cdf_gumbel2_Q (double x, double a, double b)
Function: double gsl_cdf_gumbel2_Pinv (double P, double a, double b)
Function: double gsl_cdf_gumbel2_Qinv (double Q, double a, double b)

  These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Type-2 Gumbel distribution with parameters a and b.