


The Exponential Power Distribution
==================================

.. function:: gsl_ran_exppow(a, b)

 This function returns a random variate from :index:`exponential power
 distribution` with scale parameter ``a`` and exponent ``b``.
 The distribution is,

 .. math::
   p(x) dx = {1 \over 2 a \Gamma(1+1/b)} \exp(-|x/a|^b) dx

 for :math:`x \geq 0`. For :math:`b = 1` this reduces to the Laplace distribution.
 For :math:`b = 2` it has the same form as a Gaussian distribution, but with
 :math:`a = \sqrt{2} \sigma`.

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

 This function computes the probability density :math:`p(x)` at :math:`x` for an
 exponential power distribution with scale parameter ``a`` and exponent
 ``b``, using the formula given above.

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

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

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