cauchy_cdf.m

similer program for matlab

## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2004, 2005, 2006,
##               2007 Kurt Hornik
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or (at
## your option) any later version.
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## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {} cauchy_cdf (@var{x}, @var{lambda}, @var{sigma})
## For each element of @var{x}, compute the cumulative distribution
## function (CDF) at @var{x} of the Cauchy distribution with location
## parameter @var{lambda} and scale parameter @var{sigma}.  Default
## values are @var{lambda} = 0, @var{sigma} = 1. 
## @end deftypefn

## Author: KH <[e-mail]>
## Description: CDF of the Cauchy distribution

function cdf = cauchy_cdf (x, location, scale)

  if (! (nargin == 1 || nargin == 3))
    print_usage ();
  endif

  if (nargin == 1)
    location = 0;
    scale = 1;
  endif

  if (!isscalar (location) || !isscalar (scale)) 
    [retval, x, location, scale] = common_size (x, location, scale);
    if (retval > 0)
      error ("cauchy_cdf: x, lambda and sigma must be of common size or scalar");
    endif
  endif

  sz = size (x);
  cdf = NaN * ones (sz);

  k = find ((x > -Inf) & (x < Inf) & (location > -Inf) &
            (location < Inf) & (scale > 0) & (scale < Inf));
  if (any (k))
    if (isscalar (location) && isscalar (scale)) 
      cdf(k) = 0.5 + atan ((x(k) - location) ./ scale) / pi;
    else
      cdf(k) = 0.5 + atan ((x(k) - location(k)) ./ scale(k)) / pi;
    endif
  endif

endfunction