Mercurial > octave-libtiff
view scripts/statistics/distributions/cauchy_pdf.m @ 20174:d9341b422488 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed statistics/ and @ftp/ in scripts directory.
* scripts/@ftp/ascii.m, scripts/@ftp/binary.m, scripts/@ftp/cd.m,
scripts/@ftp/dir.m, scripts/@ftp/ftp.m, scripts/@ftp/mget.m,
scripts/@ftp/mput.m, scripts/statistics/base/center.m,
scripts/statistics/base/cloglog.m, scripts/statistics/base/cov.m,
scripts/statistics/base/gls.m, scripts/statistics/base/histc.m,
scripts/statistics/base/iqr.m, scripts/statistics/base/kendall.m,
scripts/statistics/base/kurtosis.m, scripts/statistics/base/logit.m,
scripts/statistics/base/lscov.m, scripts/statistics/base/mahalanobis.m,
scripts/statistics/base/mean.m, scripts/statistics/base/meansq.m,
scripts/statistics/base/median.m, scripts/statistics/base/mode.m,
scripts/statistics/base/moment.m, scripts/statistics/base/ols.m,
scripts/statistics/base/ppplot.m, scripts/statistics/base/prctile.m,
scripts/statistics/base/probit.m, scripts/statistics/base/range.m,
scripts/statistics/base/ranks.m, scripts/statistics/base/run_count.m,
scripts/statistics/base/runlength.m, scripts/statistics/base/skewness.m,
scripts/statistics/base/spearman.m, scripts/statistics/base/statistics.m,
scripts/statistics/base/std.m, scripts/statistics/base/table.m,
scripts/statistics/base/var.m, scripts/statistics/base/zscore.m,
scripts/statistics/distributions/betainv.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/cauchy_cdf.m,
scripts/statistics/distributions/cauchy_inv.m,
scripts/statistics/distributions/cauchy_pdf.m,
scripts/statistics/distributions/chi2cdf.m,
scripts/statistics/distributions/chi2inv.m,
scripts/statistics/distributions/chi2pdf.m,
scripts/statistics/distributions/discrete_cdf.m,
scripts/statistics/distributions/discrete_inv.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/empirical_cdf.m,
scripts/statistics/distributions/empirical_inv.m,
scripts/statistics/distributions/empirical_pdf.m,
scripts/statistics/distributions/expcdf.m,
scripts/statistics/distributions/expinv.m,
scripts/statistics/distributions/exppdf.m,
scripts/statistics/distributions/finv.m,
scripts/statistics/distributions/fpdf.m,
scripts/statistics/distributions/gamcdf.m,
scripts/statistics/distributions/gaminv.m,
scripts/statistics/distributions/gampdf.m,
scripts/statistics/distributions/geoinv.m,
scripts/statistics/distributions/geopdf.m,
scripts/statistics/distributions/hygecdf.m,
scripts/statistics/distributions/hygeinv.m,
scripts/statistics/distributions/hygepdf.m,
scripts/statistics/distributions/kolmogorov_smirnov_cdf.m,
scripts/statistics/distributions/laplace_cdf.m,
scripts/statistics/distributions/laplace_inv.m,
scripts/statistics/distributions/laplace_pdf.m,
scripts/statistics/distributions/logistic_inv.m,
scripts/statistics/distributions/logncdf.m,
scripts/statistics/distributions/logninv.m,
scripts/statistics/distributions/lognpdf.m,
scripts/statistics/distributions/nbincdf.m,
scripts/statistics/distributions/nbininv.m,
scripts/statistics/distributions/nbinpdf.m,
scripts/statistics/distributions/nbinrnd.m,
scripts/statistics/distributions/normcdf.m,
scripts/statistics/distributions/norminv.m,
scripts/statistics/distributions/normpdf.m,
scripts/statistics/distributions/poisscdf.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poisspdf.m,
scripts/statistics/distributions/stdnormal_cdf.m,
scripts/statistics/distributions/stdnormal_pdf.m,
scripts/statistics/distributions/tcdf.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/tpdf.m,
scripts/statistics/distributions/unidcdf.m,
scripts/statistics/distributions/unidinv.m,
scripts/statistics/distributions/unidpdf.m,
scripts/statistics/distributions/unidrnd.m,
scripts/statistics/distributions/unifcdf.m,
scripts/statistics/distributions/unifinv.m,
scripts/statistics/distributions/wblcdf.m,
scripts/statistics/distributions/wblinv.m,
scripts/statistics/distributions/wblpdf.m,
scripts/statistics/distributions/wienrnd.m,
scripts/statistics/models/private/logistic_regression_derivatives.m,
scripts/statistics/models/private/logistic_regression_likelihood.m,
scripts/statistics/tests/anova.m,
scripts/statistics/tests/chisquare_test_homogeneity.m,
scripts/statistics/tests/chisquare_test_independence.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/f_test_regression.m,
scripts/statistics/tests/hotelling_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/mcnemar_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/run_test.m,
scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m,
scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 10 May 2015 16:07:41 -0700 |
parents | 9fc020886ae9 |
children | 516bb87ea72e |
line wrap: on
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## Copyright (C) 2012 Rik Wehbring ## Copyright (C) 1995-2015 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)