Gamma
=====

The gamma distribution has a probability density function defined by

.. math::
    :label: eqn-random-gamma-pdf

    f_X(x;\alpha,\beta) =
    \begin{cases}
        \frac{
            x^{\alpha-1}
        }{
            \Gamma(\alpha) \beta^\alpha
        }
        e^{-x / \beta}                  & x \ge 0 \\
        0                               & \text{else}.
    \end{cases}

.. qplot:: random random/random.c
    :args: -d gamma -A 4.5 -B 1
    :width: 80%
    :name: fig-gamma
    :caption: Gamma distribution with :math:`\alpha=4.5` and :math:`\beta=1`

Interface
~~~~~~~~~

Gamma random number generator interface:

.. code-block:: c

    // generate gamma random variable
    float randgammaf(float _alpha,
                     float _beta);

    // compute a gamma probability density
    float randgammaf_pdf(float _x,
                         float _alpha,
                         float _beta);

    // compute a gamma cumulative distribution
    float randgammaf_cdf(float _x,
                         float _alpha,
                         float _beta);