Mercurial > octave-nkf
view scripts/statistics/distributions/cauchy_cdf.m @ 14138:72c96de7a403 stable
maint: update copyright notices for 2012
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 02 Jan 2012 14:25:41 -0500 |
parents | 19b9f17d22af |
children | f3d52523cde1 |
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## Copyright (C) 2012 Rik Wehbring ## Copyright (C) 1995-2012 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_cdf (@var{x}) ## @deftypefnx {Function File} {} cauchy_cdf (@var{x}, @var{location}, @var{scale}) ## For each element of @var{x}, compute the cumulative distribution ## function (CDF) at @var{x} of the Cauchy distribution with location ## parameter @var{location} and scale parameter @var{scale}. Default ## values are @var{location} = 0, @var{scale} = 1. ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: CDF of the Cauchy distribution function cdf = cauchy_cdf (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_cdf: X, LOCATION, and SCALE must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (location) || iscomplex (scale)) error ("cauchy_cdf: X, LOCATION, and SCALE must not be complex"); endif if (isa (x, "single") || isa (location, "single") || isa (scale, "single")); cdf = NaN (size (x), "single"); else cdf = NaN (size (x)); endif k = !isinf (location) & (scale > 0) & (scale < Inf); if (isscalar (location) && isscalar (scale)) cdf = 0.5 + atan ((x - location) / scale) / pi; else cdf(k) = 0.5 + atan ((x(k) - location(k)) ./ scale(k)) / pi; endif endfunction %!shared x,y %! x = [-1 0 0.5 1 2]; %! y = 1/pi * atan ((x-1) / 2) + 1/2; %!assert(cauchy_cdf (x, ones(1,5), 2*ones(1,5)), y); %!assert(cauchy_cdf (x, 1, 2*ones(1,5)), y); %!assert(cauchy_cdf (x, ones(1,5), 2), y); %!assert(cauchy_cdf (x, [-Inf 1 NaN 1 Inf], 2), [NaN y(2) NaN y(4) NaN]); %!assert(cauchy_cdf (x, 1, 2*[0 1 NaN 1 Inf]), [NaN y(2) NaN y(4) NaN]); %!assert(cauchy_cdf ([x(1:2) NaN x(4:5)], 1, 2), [y(1:2) NaN y(4:5)]); %% Test class of input preserved %!assert(cauchy_cdf ([x, NaN], 1, 2), [y, NaN]); %!assert(cauchy_cdf (single([x, NaN]), 1, 2), single([y, NaN]), eps("single")); %!assert(cauchy_cdf ([x, NaN], single(1), 2), single([y, NaN]), eps("single")); %!assert(cauchy_cdf ([x, NaN], 1, single(2)), single([y, NaN]), eps("single")); %% Test input validation %!error cauchy_cdf () %!error cauchy_cdf (1,2) %!error cauchy_cdf (1,2,3,4) %!error cauchy_cdf (ones(3),ones(2),ones(2)) %!error cauchy_cdf (ones(2),ones(3),ones(2)) %!error cauchy_cdf (ones(2),ones(2),ones(3)) %!error cauchy_cdf (i, 2, 2) %!error cauchy_cdf (2, i, 2) %!error cauchy_cdf (2, 2, i)