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% STK_DISTRIB_STUDENT_CDF [STK internal]
% Copyright Notice
%
% Copyright (C) 2018 CentraleSupelec
% Copyright (C) 2013, 2014 SUPELEC
%
% Author: Julien Bect <julien.bect@centralesupelec.fr>
%
% This code is very loosely based on Octave's tcdf function:
% ## Copyright (C) 2013 Julien Bect
% ## Copyright (C) 2012 Rik Wehbring
% ## Copyright (C) 1995-2012 Kurt Hornik
% Copying Permission Statement
%
% This file is part of
%
% STK: a Small (Matlab/Octave) Toolbox for Kriging
% (https://github.com/stk-kriging/stk/)
%
% STK 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.
%
% STK 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 STK. If not, see <http://www.gnu.org/licenses/>.
function [p, q] = stk_distrib_student_cdf (z, nu, mu, sigma)
if nargin > 2,
z = bsxfun (@minus, z, mu);
end
if nargin > 3,
z = bsxfun (@rdivide, z, sigma);
end
xx = z .^ 2;
[z, xx, nu] = stk_commonsize (z, xx, nu);
% Return NaN for negative values of nu (or nu == NaN, or x == NaN)
p = nan (size (z));
q = nan (size (z));
k0 = (nu > 0) & (~ isnan (z));
% Gaussian case (nu = +inf)
k_inf = isinf (nu); k = k0 & k_inf;
[p(k), q(k)] = stk_distrib_normal_cdf (z(k));
k0 = k0 & (~ k_inf);
kp = (z > 0);
kn = k0 & (~ kp);
kp = k0 & kp;
k_big_abs = (xx > nu);
% Student case (nu < +inf) for positive x: compute q first, then p = 1 - q
k = kp & k_big_abs;
q(k) = betainc (nu(k) ./ (nu(k) + xx(k)), nu(k)/2, 1/2) / 2;
k = kp & (~ k_big_abs);
q(k) = 0.5 * (1 - betainc (xx(k) ./ (nu(k) + xx(k)), 1/2, nu(k)/2));
p(kp) = 1 - q(kp);
% Student case (nu < +inf) for negative x: compute p first, then q = 1 - p
k = kn & k_big_abs;
p(k) = betainc (nu(k) ./ (nu(k) + xx(k)), nu(k)/2, 1/2) / 2;
k = kn & (~ k_big_abs);
p(k) = 0.5 * (1 - betainc (xx(k) ./ (nu(k) + xx(k)), 1/2, nu(k)/2));
q(kn) = 1 - p(kn);
end % function
%!assert (stk_isequal_tolrel ( ...
%! stk_distrib_student_cdf ([-1; 0; 1], [1 2], 0, [1 10]), ...
%! [0.25, ... % tcdf ((-1 - 0)/1, 1)
%! 4.6473271920707004e-01; ... % tcdf ((-1 - 0)/10, 2)
%! 0.50, ... % tcdf (( 0 - 0)/1, 1)
%! 0.50; ... % tcdf (( 0 - 0)/10, 2)
%! 0.75, ... % tcdf (( 1 - 0)/1, 1)
%! 5.3526728079292996e-01 ... % tcdf (( 1 - 0)/10, 2)
%! ], 4 * eps))
%!test
%! [p, q] = stk_distrib_student_cdf (1e10, 2);
%! assert (isequal (p, 1.0));
%! assert (stk_isequal_tolrel (q, 4.999999999999999999925e-21, 10 * eps));
%!assert (isequal (stk_distrib_student_cdf (0.0, 1), 0.5));
%!assert (isequal (stk_distrib_student_cdf (inf, 1), 1.0));
%!assert (isequal (stk_distrib_student_cdf (-inf, 1), 0.0));
%!assert (isnan (stk_distrib_student_cdf (nan, 1)));
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