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maint: Update copyright notices for 2015.
author John W. Eaton <jwe@octave.org>
date Wed, 11 Feb 2015 14:19:08 -0500
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1 ## Copyright (C) 2012 Rik Wehbring
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2 ## Copyright (C) 1995-2015 Kurt Hornik
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {} tinv (@var{x}, @var{n})
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22 ## For each element of @var{x}, compute the quantile (the inverse of
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23 ## the CDF) at @var{x} of the t (Student) distribution with @var{n}
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24 ## degrees of freedom. This function is analogous to looking in a table
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25 ## for the t-value of a single-tailed distribution.
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26 ## @end deftypefn
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27
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28 ## For very large n, the "correct" formula does not really work well,
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29 ## and the quantiles of the standard normal distribution are used
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30 ## directly.
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31
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32 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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33 ## Description: Quantile function of the t distribution
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34
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35 function inv = tinv (x, n)
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36
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37 if (nargin != 2)
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38 print_usage ();
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39 endif
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40
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41 if (!isscalar (n))
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42 [retval, x, n] = common_size (x, n);
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43 if (retval > 0)
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44 error ("tinv: X and N must be of common size or scalars");
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45 endif
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46 endif
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47
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48 if (iscomplex (x) || iscomplex (n))
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49 error ("tinv: X and N must not be complex");
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50 endif
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51
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52 if (isa (x, "single") || isa (n, "single"))
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53 inv = NaN (size (x), "single");
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54 else
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55 inv = NaN (size (x));
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56 endif
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57
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58 k = (x == 0) & (n > 0);
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59 inv(k) = -Inf;
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60
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61 k = (x == 1) & (n > 0);
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62 inv(k) = Inf;
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63
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64 if (isscalar (n))
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65 k = (x > 0) & (x < 1);
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66 if ((n > 0) && (n < 10000))
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67 inv(k) = (sign (x(k) - 1/2)
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68 .* sqrt (n * (1 ./ betainv (2*min (x(k), 1 - x(k)),
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69 n/2, 1/2) - 1)));
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70 elseif (n >= 10000)
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71 ## For large n, use the quantiles of the standard normal
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72 inv(k) = stdnormal_inv (x(k));
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73 endif
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74 else
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75 k = (x > 0) & (x < 1) & (n > 0) & (n < 10000);
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76 inv(k) = (sign (x(k) - 1/2)
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77 .* sqrt (n(k) .* (1 ./ betainv (2*min (x(k), 1 - x(k)),
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78 n(k)/2, 1/2) - 1)));
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79
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80 ## For large n, use the quantiles of the standard normal
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81 k = (x > 0) & (x < 1) & (n >= 10000);
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82 inv(k) = stdnormal_inv (x(k));
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83 endif
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84
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85 endfunction
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86
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87
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88 %!shared x
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89 %! x = [-1 0 0.5 1 2];
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90 %!assert (tinv (x, ones (1,5)), [NaN -Inf 0 Inf NaN])
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91 %!assert (tinv (x, 1), [NaN -Inf 0 Inf NaN], eps)
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92 %!assert (tinv (x, [1 0 NaN 1 1]), [NaN NaN NaN Inf NaN], eps)
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93 %!assert (tinv ([x(1:2) NaN x(4:5)], 1), [NaN -Inf NaN Inf NaN])
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94
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95 %% Test class of input preserved
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96 %!assert (tinv ([x, NaN], 1), [NaN -Inf 0 Inf NaN NaN], eps)
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97 %!assert (tinv (single ([x, NaN]), 1), single ([NaN -Inf 0 Inf NaN NaN]), eps ("single"))
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98 %!assert (tinv ([x, NaN], single (1)), single ([NaN -Inf 0 Inf NaN NaN]), eps ("single"))
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99
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100 %% Test input validation
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101 %!error tinv ()
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102 %!error tinv (1)
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103 %!error tinv (1,2,3)
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104 %!error tinv (ones (3), ones (2))
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105 %!error tinv (ones (2), ones (3))
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106 %!error tinv (i, 2)
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107 %!error tinv (2, i)
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108