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scripts/statistics/distributions/cauchy_pdf.m

changeset 10289: 4b124317dc38
parent:93c65f2a5668
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (28 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2004, 2005, 2006,

     2##               2007 Kurt Hornik

     3##

     4## This file is part of Octave.

     5##

     6## Octave is free software; you can redistribute it and/or modify it

     7## under the terms of the GNU General Public License as published by

     8## the Free Software Foundation; either version 3 of the License, or (at

     9## your option) any later version.

    10##

    11## Octave is distributed in the hope that it will be useful, but

    12## WITHOUT ANY WARRANTY; without even the implied warranty of

    13## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

    14## General Public License for more details.

    15##

    16## You should have received a copy of the GNU General Public License

    17## along with Octave; see the file COPYING.  If not, see

    18## <http://www.gnu.org/licenses/>.

    19

    20## -*- texinfo -*-

    21## @deftypefn {Function File} {} cauchy_pdf (@var{x}, @var{lambda}, @var{sigma})

    22## For each element of @var{x}, compute the probability density function

    23## (PDF) at @var{x} of the Cauchy distribution with location parameter

    24## @var{lambda} and scale parameter @var{sigma} > 0.  Default values are

    25## @var{lambda} = 0, @var{sigma} = 1. 

    26## @end deftypefn

    27

    28## Author: KH <Kurt.Hornik@wu-wien.ac.at>

    29## Description: PDF of the Cauchy distribution

    30

    31function pdf = cauchy_pdf (x, location, scale)

    32

    33  if (! (nargin == 1 || nargin == 3))

    34    print_usage ();

    35  endif

    36

    37  if (nargin == 1)

    38    location = 0;

    39    scale = 1;

    40  endif

    41

    42  if (!isscalar (location) || !isscalar (scale)) 

    43    [retval, x, location, scale] = common_size (x, location, scale);

    44    if (retval > 0)

    45      error ("cauchy_pdf: x, lambda and sigma must be of common size or scalar");

    46    endif

    47  endif

    48

    49  sz = size (x);

    50  pdf = NaN * ones (sz);

    51

    52  k = find ((x > -Inf) & (x < Inf) & (location > -Inf) &

    53            (location < Inf) & (scale > 0) & (scale < Inf));

    54  if (any (k))

    55    if (isscalar (location) && isscalar (scale)) 

    56      pdf(k) = ((1 ./ (1 + ((x(k) - location) ./ scale) .^ 2))

    57		/ pi ./ scale);

    58    else

    59      pdf(k) = ((1 ./ (1 + ((x(k) - location(k)) ./ scale(k)) .^ 2))

    60		/ pi ./ scale(k));

    61    endif

    62  endif

    63

    64endfunction