


The Gamma Distribution
======================

.. function:: gsl_ran_gamma(a, b)

 This function returns a random variate from the :index:`gamma
 distribution`. The distribution function is,

 .. math::
   p(x) dx = {1 \over \Gamma(a) b^a} x^{a-1} e^{-x/b} dx

 for :math:`x > 0`.

 The gamma distribution with an integer parameter ``a`` is known as
 the Erlang distribution.

 The variates are computed using the Marsaglia-Tsang fast gamma method.

.. function:: gsl_ran_gamma_knuth(a, b)

 This function returns a gamma variate using the algorithms from Knuth
 (vol 2).

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

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

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

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

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

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

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