


The Cauchy Distribution
========================

.. function:: gsl_ran_cauchy(a)

 This function returns a random variate from the :index:`Cauchy
 distribution` with scale parameter ``a``. The probability
 distribution for Cauchy random variates is,

 .. math::
   p(x) dx = {1 \over a\pi (1 + (x/a)^2) } dx

 for :math:`x` in the range :math:`-\infty` to :math:`+\infty`. The Cauchy distribution
 is also known as the Lorentz distribution.

.. function:: gsl_ran_cauchy_pdf(x, a)

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

.. function:: gsl_ran_cauchy_P(x, a)

.. function:: gsl_ran_cauchy_Q(x, a)

.. function:: gsl_ran_cauchy_Pinv(P, a)

.. function:: gsl_ran_cauchy_Qinv(Q, a)

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