Mercurial > octave-nkf
view scripts/statistics/distributions/tcdf.m @ 20209: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 |
line wrap: on
line source
## Copyright (C) 2013-2015 Julien Bect ## 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} {} tcdf (@var{x}, @var{n}) ## For each element of @var{x}, compute the cumulative distribution function ## (CDF) at @var{x} of the t (Student) distribution with ## @var{n} degrees of freedom. ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: CDF of the t distribution function cdf = tcdf (x, n) if (nargin != 2) print_usage (); endif if (! isscalar (n)) [retval, x, n] = common_size (x, n); if (retval > 0) error ("tcdf: X and N must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (n)) error ("tcdf: X and N must not be complex"); endif if (isa (x, "single") || isa (n, "single")) cdf = zeros (size (x), "single"); else cdf = zeros (size (x)); endif k = ! isinf (x) & (n > 0); xx = x .^ 2; x_big_abs = (xx > n); ## deal with the case "abs(x) big" kk = k & x_big_abs; if (isscalar (n)) cdf(kk) = betainc (n ./ (n + xx(kk)), n/2, 1/2) / 2; else cdf(kk) = betainc (n(kk) ./ (n(kk) + xx(kk)), n(kk)/2, 1/2) / 2; endif ## deal with the case "abs(x) small" kk = k & !x_big_abs; if (isscalar (n)) cdf(kk) = 0.5 * (1 - betainc (xx(kk) ./ (n + xx(kk)), 1/2, n/2)); else cdf(kk) = 0.5 * (1 - betainc (xx(kk) ./ (n(kk) + xx(kk)), 1/2, n(kk)/2)); endif k &= (x > 0); if (any (k(:))) cdf(k) = 1 - cdf(k); endif k = isnan (x) | !(n > 0); cdf(k) = NaN; k = (x == Inf) & (n > 0); cdf(k) = 1; endfunction %!shared x,y %! x = [-Inf 0 1 Inf]; %! y = [0 1/2 3/4 1]; %!assert (tcdf (x, ones (1,4)), y, eps) %!assert (tcdf (x, 1), y, eps) %!assert (tcdf (x, [0 1 NaN 1]), [NaN 1/2 NaN 1], eps) %!assert (tcdf ([x(1:2) NaN x(4)], 1), [y(1:2) NaN y(4)], eps) ## Test class of input preserved %!assert (tcdf ([x, NaN], 1), [y, NaN], eps) %!assert (tcdf (single ([x, NaN]), 1), single ([y, NaN]), eps ("single")) %!assert (tcdf ([x, NaN], single (1)), single ([y, NaN]), eps ("single")) ## Test input validation %!error tcdf () %!error tcdf (1) %!error tcdf (1,2,3) %!error tcdf (ones (3), ones (2)) %!error tcdf (ones (2), ones (3)) %!error tcdf (i, 2) %!error tcdf (2, i) ## Check some reference values %!shared tol_rel %! tol_rel = 10 * eps; ## check accuracy for small positive values %!assert (tcdf (10^(-10), 2.5), 0.50000000003618087, -tol_rel) %!assert (tcdf (10^(-11), 2.5), 0.50000000000361809, -tol_rel) %!assert (tcdf (10^(-12), 2.5), 0.50000000000036181, -tol_rel) %!assert (tcdf (10^(-13), 2.5), 0.50000000000003618, -tol_rel) %!assert (tcdf (10^(-14), 2.5), 0.50000000000000362, -tol_rel) %!assert (tcdf (10^(-15), 2.5), 0.50000000000000036, -tol_rel) %!assert (tcdf (10^(-16), 2.5), 0.50000000000000004, -tol_rel) ## check accuracy for large negative values %!assert (tcdf (-10^1, 2.5), 2.2207478836537124e-03, -tol_rel) %!assert (tcdf (-10^2, 2.5), 7.1916492116661878e-06, -tol_rel) %!assert (tcdf (-10^3, 2.5), 2.2747463948307452e-08, -tol_rel) %!assert (tcdf (-10^4, 2.5), 7.1933970159922115e-11, -tol_rel) %!assert (tcdf (-10^5, 2.5), 2.2747519231756221e-13, -tol_rel) ## # Reference values obtained using Python 2.7.4 and mpmath 0.17 ## ## from mpmath import * ## ## mp.dps = 100 ## ## def F(x_in, nu_in): ## x = mpf(x_in); ## nu = mpf(nu_in); ## t = nu / (nu + x*x) ## a = nu / 2 ## b = mpf(0.5) ## F = betainc(a, b, 0, t, regularized=True) / 2 ## if (x > 0): ## F = 1 - F ## return F ## ## nu = 2.5 ## ## for i in range(1, 6): ## x = - power(mpf(10), mpf(i)) ## print "%%!assert (tcdf (-10^%d, 2.5), %s, -eps)" \ ## % (i, nstr(F(x, nu), 17)) ## ## for i in range(10, 17): ## x = power(mpf(10), -mpf(i)) ## print "%%!assert (tcdf (10^(-%d), 2.5), %s, -eps)" \ ## % (i, nstr(F(x, nu), 17))