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### 20.26 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.

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