


The Type-1 Gumbel Distribution
==============================

.. function:: gsl_ran_gumbel1(a, b)

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

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

 for :math:`-\infty < x < \infty`.

.. function:: gsl_ran_gumbel1_pdf(x, a, b)

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

.. function:: gsl_cdf_gumbel1_P(x, a, b)

.. function:: gsl_cdf_gumbel1_Q(x, a, b)

.. function:: gsl_cdf_gumbel1_Pinv(P, a, b)

.. function:: gsl_cdf_gumbel1_Qinv(Q, a, b)

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