


The Rayleigh Distribution
=========================

.. function:: gsl_ran_rayleigh(sigma)

 This function returns a random variate from the :index:`Rayleigh
 distribution` with scale parameter ``sigma``.
 The distribution is,

 .. math::
   p(x) dx = {x \over \sigma^2} \exp(- x^2/(2 \sigma^2)) dx

 for :math:`x > 0`.

.. function:: gsl_ran_rayleigh_pdf(x, sigma)

 This function computes the probability density :math:`p(x)` at :math:`x` for a
 Rayleigh distribution with scale parameter ``sigma``, using the formula
 given above.

.. function:: gsl_ran_rayleigh_P(x, sigma)

.. function:: gsl_ran_rayleigh_Q(x, sigma)

.. function:: gsl_ran_rayleigh_Pinv(P, sigma)

.. function:: gsl_ran_rayleigh_Qinv(Q, sigma)

 These functions compute the cumulative distribution functions
 :math:`P(x), Q(x)` and their inverses for the Rayleigh distribution with
 scale parameter ``sigma``.
