


The Gaussian Tail Distribution
==============================

.. function:: gsl_ran_gaussian_tail(a, sigma)

 This function provides random variates from the upper tail of a
 Gaussian distribution with standard deviation ``sigma``. The values
 returned are larger than the lower limit ``a``, which must be positive.
 The method is based on Marsaglia's famous rectangle-wedge-tail
 algorithm (Ann. Math. Stat. 32, 894-899 (1961)), with this aspect
 explained in Knuth, v2, 3rd ed, p139,586 (exercise 11).

 The probability distribution for Gaussian tail random variates is,

 .. math::
   p(x) dx = {1 \over N(a;\sigma) \sqrt{2 \pi \sigma^2}}
     \exp (- x^2/(2 \sigma^2)) dx

 for :math:`x > a` where :math:`N(a;\sigma)` is the normalization constant,

 .. math::
   N(a;\sigma) = (1/2) \operatorname{erfc}(a / \sqrt{2 \sigma^2}).

.. function:: gsl_ran_gaussian_tail_pdf(x, a, sigma)

 This function computes the probability density :math:`p(x)` at :math:`x` for a
 Gaussian tail distribution with standard deviation ``sigma`` and lower
 limit ``a``, using the formula given above.

.. function:: gsl_ran_ugaussian_tail(a)

.. function:: gsl_ran_ugaussian_tail_pdf(x, a)

 These functions compute results for the tail of a unit Gaussian
 distribution. They are equivalent to the functions above with a
 standard deviation of one, ``sigma`` = 1.
