The Type-2 Gumbel Distribution¶
-
gsl_ran_gumbel2
(a, 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 \(-\infty < x < \infty\).
-
gsl_ran_gumbel2_pdf
(x, a, b)¶ This function computes the probability density \(p(x)\) at \(x\) for a Type-2 Gumbel distribution with parameters
a
andb
, using the formula given above.
-
gsl_cdf_gumbel2_P
(x, a, b)¶
-
gsl_cdf_gumbel2_Q
(x, a, b)¶
-
gsl_cdf_gumbel2_Pinv
(P, a, b)¶
-
gsl_cdf_gumbel2_Qinv
(Q, a, b)¶ These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the Type-2 Gumbel distribution with parameters
a
andb
.