Mercurial > octave-nkf
view scripts/statistics/distributions/cauchy_pdf.m @ 17744:d63878346099
maint: Update copyright notices for release.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Wed, 23 Oct 2013 22:09:27 -0400 |
parents | f3d52523cde1 |
children | 4197fc428c7d |
line wrap: on
line source
## Copyright (C) 2012 Rik Wehbring ## Copyright (C) 1995-2013 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. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## 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_pdf (@var{x}) ## @deftypefnx {Function File} {} cauchy_pdf (@var{x}, @var{location}, @var{scale}) ## For each element of @var{x}, compute the probability density function ## (PDF) at @var{x} of the Cauchy distribution with location parameter ## @var{location} and scale parameter @var{scale} > 0. Default values are ## @var{location} = 0, @var{scale} = 1. ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: PDF of the Cauchy distribution function pdf = cauchy_pdf (x, location = 0, scale = 1) if (nargin != 1 && nargin != 3) print_usage (); endif if (!isscalar (location) || !isscalar (scale)) [retval, x, location, scale] = common_size (x, location, scale); if (retval > 0) error ("cauchy_pdf: X, LOCATION, and SCALE must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (location) || iscomplex (scale)) error ("cauchy_pdf: X, LOCATION, and SCALE must not be complex"); endif if (isa (x, "single") || isa (location, "single") || isa (scale, "single")) pdf = NaN (size (x), "single"); else pdf = NaN (size (x)); endif k = !isinf (location) & (scale > 0) & (scale < Inf); if (isscalar (location) && isscalar (scale)) pdf = ((1 ./ (1 + ((x - location) / scale) .^ 2)) / pi / scale); else pdf(k) = ((1 ./ (1 + ((x(k) - location(k)) ./ scale(k)) .^ 2)) / pi ./ scale(k)); endif endfunction %!shared x,y %! x = [-1 0 0.5 1 2]; %! y = 1/pi * ( 2 ./ ((x-1).^2 + 2^2) ); %!assert (cauchy_pdf (x, ones (1,5), 2*ones (1,5)), y) %!assert (cauchy_pdf (x, 1, 2*ones (1,5)), y) %!assert (cauchy_pdf (x, ones (1,5), 2), y) %!assert (cauchy_pdf (x, [-Inf 1 NaN 1 Inf], 2), [NaN y(2) NaN y(4) NaN]) %!assert (cauchy_pdf (x, 1, 2*[0 1 NaN 1 Inf]), [NaN y(2) NaN y(4) NaN]) %!assert (cauchy_pdf ([x, NaN], 1, 2), [y, NaN]) %% Test class of input preserved %!assert (cauchy_pdf (single ([x, NaN]), 1, 2), single ([y, NaN]), eps ("single")) %!assert (cauchy_pdf ([x, NaN], single (1), 2), single ([y, NaN]), eps ("single")) %!assert (cauchy_pdf ([x, NaN], 1, single (2)), single ([y, NaN]), eps ("single")) %% Cauchy (0,1) == Student's T distribution with 1 DOF %!test %! x = rand (10, 1); %! assert (cauchy_pdf (x, 0, 1), tpdf (x, 1), eps); %% Test input validation %!error cauchy_pdf () %!error cauchy_pdf (1,2) %!error cauchy_pdf (1,2,3,4) %!error cauchy_pdf (ones (3), ones (2), ones (2)) %!error cauchy_pdf (ones (2), ones (3), ones (2)) %!error cauchy_pdf (ones (2), ones (2), ones (3)) %!error cauchy_pdf (i, 2, 2) %!error cauchy_pdf (2, i, 2) %!error cauchy_pdf (2, 2, i)