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annotate scripts/statistics/distributions/fpdf.m @ 20830:b65888ec820e draft default tip gccjit

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dmalcom gcc jit import
author Stefan Mahr <dac922@gmx.de>
date Fri, 27 Feb 2015 16:59:36 +0100
parents d9341b422488
children
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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} {} fpdf (@var{x}, @var{m}, @var{n})
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22 ## For each element of @var{x}, compute the probability density function (PDF)
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23 ## at @var{x} of the F distribution with @var{m} and @var{n} degrees of freedom.
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24 ## @end deftypefn
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25
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26 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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27 ## Description: PDF of the F distribution
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28
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29 function pdf = fpdf (x, m, n)
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30
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31 if (nargin != 3)
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32 print_usage ();
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33 endif
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34
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35 if (! isscalar (m) || ! isscalar (n))
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36 [retval, x, m, n] = common_size (x, m, n);
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37 if (retval > 0)
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38 error ("fpdf: X, M, and N must be of common size or scalars");
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39 endif
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40 endif
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41
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42 if (iscomplex (x) || iscomplex (m) || iscomplex (n))
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43 error ("fpdf: X, M, and N must not be complex");
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44 endif
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45
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46 if (isa (x, "single") || isa (m, "single") || isa (n, "single"))
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47 pdf = zeros (size (x), "single");
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48 else
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49 pdf = zeros (size (x));
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50 endif
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51
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52 k = isnan (x) | !(m > 0) | !(m < Inf) | !(n > 0) | !(n < Inf);
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53 pdf(k) = NaN;
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54
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55 k = (x > 0) & (x < Inf) & (m > 0) & (m < Inf) & (n > 0) & (n < Inf);
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56 if (isscalar (m) && isscalar (n))
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57 tmp = m / n * x(k);
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58 pdf(k) = (exp ((m/2 - 1) * log (tmp)
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59 - ((m + n) / 2) * log (1 + tmp))
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60 * (m / n) ./ beta (m/2, n/2));
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61 else
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62 tmp = m(k) .* x(k) ./ n(k);
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63 pdf(k) = (exp ((m(k)/2 - 1) .* log (tmp)
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64 - ((m(k) + n(k)) / 2) .* log (1 + tmp))
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65 .* (m(k) ./ n(k)) ./ beta (m(k)/2, n(k)/2));
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66 endif
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67
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68 endfunction
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69
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70
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71 ## F (x, 1, m) == T distribution (sqrt (x), m) / sqrt (x)
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72 %!test
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73 %! x = rand (10,1);
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74 %! x = x(x > 0.1 & x < 0.9);
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75 %! y = tpdf (sqrt (x), 2) ./ sqrt (x);
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76 %! assert (fpdf (x, 1, 2), y, 5*eps);
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77
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78 %!shared x,y
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79 %! x = [-1 0 0.5 1 2];
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80 %! y = [0 0 4/9 1/4 1/9];
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81 %!assert (fpdf (x, 2*ones (1,5), 2*ones (1,5)), y, eps)
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82 %!assert (fpdf (x, 2, 2*ones (1,5)), y, eps)
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83 %!assert (fpdf (x, 2*ones (1,5), 2), y, eps)
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84 %!assert (fpdf (x, [0 NaN Inf 2 2], 2), [NaN NaN NaN y(4:5)], eps)
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85 %!assert (fpdf (x, 2, [0 NaN Inf 2 2]), [NaN NaN NaN y(4:5)], eps)
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86 %!assert (fpdf ([x, NaN], 2, 2), [y, NaN], eps)
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87
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88 ## Test class of input preserved
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89 %!assert (fpdf (single ([x, NaN]), 2, 2), single ([y, NaN]), eps ("single"))
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90 %!assert (fpdf ([x, NaN], single (2), 2), single ([y, NaN]), eps ("single"))
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91 %!assert (fpdf ([x, NaN], 2, single (2)), single ([y, NaN]), eps ("single"))
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92
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93 ## Test input validation
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94 %!error fpdf ()
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95 %!error fpdf (1)
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96 %!error fpdf (1,2)
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97 %!error fpdf (1,2,3,4)
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98 %!error fpdf (ones (3), ones (2), ones (2))
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99 %!error fpdf (ones (2), ones (3), ones (2))
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100 %!error fpdf (ones (2), ones (2), ones (3))
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101 %!error fpdf (i, 2, 2)
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102 %!error fpdf (2, i, 2)
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103 %!error fpdf (2, 2, i)
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104