X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;f=octave_packages%2Fm%2Fstatistics%2Fdistributions%2Ftinv.m;fp=octave_packages%2Fm%2Fstatistics%2Fdistributions%2Ftinv.m;h=e635a1efd9924080c11f60be4f68404720477c40;hb=1c0469ada9531828709108a4882a751d2816994a;hp=0000000000000000000000000000000000000000;hpb=63de9f36673d49121015e3695f2c336ea92bc278;p=CreaPhase.git diff --git a/octave_packages/m/statistics/distributions/tinv.m b/octave_packages/m/statistics/distributions/tinv.m new file mode 100644 index 0000000..e635a1e --- /dev/null +++ b/octave_packages/m/statistics/distributions/tinv.m @@ -0,0 +1,108 @@ +## 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 +## . + +## -*- texinfo -*- +## @deftypefn {Function File} {} tinv (@var{x}, @var{n}) +## For each element of @var{x}, compute the quantile (the inverse of +## the CDF) at @var{x} of the t (Student) distribution with @var{n} +## degrees of freedom. This function is analogous to looking in a table +## for the t-value of a single-tailed distribution. +## @end deftypefn + +## For very large n, the "correct" formula does not really work well, +## and the quantiles of the standard normal distribution are used +## directly. + +## Author: KH +## Description: Quantile function of the t distribution + +function inv = tinv (x, n) + + if (nargin != 2) + print_usage (); + endif + + if (!isscalar (n)) + [retval, x, n] = common_size (x, n); + if (retval > 0) + error ("tinv: X and N must be of common size or scalars"); + endif + endif + + if (iscomplex (x) || iscomplex (n)) + error ("tinv: X and N must not be complex"); + endif + + if (isa (x, "single") || isa (n, "single")) + inv = NaN (size (x), "single"); + else + inv = NaN (size (x)); + endif + + k = (x == 0) & (n > 0); + inv(k) = -Inf; + + k = (x == 1) & (n > 0); + inv(k) = Inf; + + if (isscalar (n)) + k = (x > 0) & (x < 1); + if ((n > 0) && (n < 10000)) + inv(k) = (sign (x(k) - 1/2) + .* sqrt (n * (1 ./ betainv (2*min (x(k), 1 - x(k)), + n/2, 1/2) - 1))); + elseif (n >= 10000) + ## For large n, use the quantiles of the standard normal + inv(k) = stdnormal_inv (x(k)); + endif + else + k = (x > 0) & (x < 1) & (n > 0) & (n < 10000); + inv(k) = (sign (x(k) - 1/2) + .* sqrt (n(k) .* (1 ./ betainv (2*min (x(k), 1 - x(k)), + n(k)/2, 1/2) - 1))); + + ## For large n, use the quantiles of the standard normal + k = (x > 0) & (x < 1) & (n >= 10000); + inv(k) = stdnormal_inv (x(k)); + endif + +endfunction + + +%!shared x +%! x = [-1 0 0.5 1 2]; +%!assert(tinv (x, ones(1,5)), [NaN -Inf 0 Inf NaN]); +%!assert(tinv (x, 1), [NaN -Inf 0 Inf NaN], eps); +%!assert(tinv (x, [1 0 NaN 1 1]), [NaN NaN NaN Inf NaN], eps); +%!assert(tinv ([x(1:2) NaN x(4:5)], 1), [NaN -Inf NaN Inf NaN]); + +%% Test class of input preserved +%!assert(tinv ([x, NaN], 1), [NaN -Inf 0 Inf NaN NaN], eps); +%!assert(tinv (single([x, NaN]), 1), single([NaN -Inf 0 Inf NaN NaN]), eps("single")); +%!assert(tinv ([x, NaN], single(1)), single([NaN -Inf 0 Inf NaN NaN]), eps("single")); + +%% Test input validation +%!error tinv () +%!error tinv (1) +%!error tinv (1,2,3) +%!error tinv (ones(3),ones(2)) +%!error tinv (ones(2),ones(3)) +%!error tinv (i, 2) +%!error tinv (2, i) +