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annotate scripts/statistics/distributions/betapdf.m @ 20038:9fc020886ae9

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maint: Clean up m-files to follow Octave coding conventions. Try to trim long lines to < 80 chars. Use '##' for single line comments. Use '(...)' around tests for if/elseif/switch/while. Abut cell indexing operator '{' next to variable. Abut array indexing operator '(' next to variable. Use space between negation operator '!' and following expression. Use two newlines between endfunction and start of %!test or %!demo code. Remove unnecessary parens grouping between short-circuit operators. Remove stray extra spaces (typos) between variables and assignment operators. Remove stray extra spaces from ends of lines.
author Rik <rik@octave.org>
date Mon, 23 Feb 2015 14:54:39 -0800
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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 ## Copyright (C) 2010 Christos Dimitrakakis
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4 ##
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5 ## This file is part of Octave.
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6 ##
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7 ## Octave is free software; you can redistribute it and/or modify it
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8 ## under the terms of the GNU General Public License as published by
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9 ## the Free Software Foundation; either version 3 of the License, or (at
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10 ## your option) any later version.
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11 ##
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12 ## Octave is distributed in the hope that it will be useful, but
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13 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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15 ## General Public License for more details.
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16 ##
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17 ## You should have received a copy of the GNU General Public License
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18 ## along with Octave; see the file COPYING. If not, see
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19 ## <http://www.gnu.org/licenses/>.
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20
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21 ## -*- texinfo -*-
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22 ## @deftypefn {Function File} {} betapdf (@var{x}, @var{a}, @var{b})
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23 ## For each element of @var{x}, compute the probability density function (PDF)
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24 ## at @var{x} of the Beta distribution with parameters @var{a} and @var{b}.
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25 ## @end deftypefn
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26
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27 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>, CD <christos.dimitrakakis@gmail.com>
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28 ## Description: PDF of the Beta distribution
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29
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30 function pdf = betapdf (x, a, b)
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31
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32 if (nargin != 3)
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33 print_usage ();
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34 endif
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35
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36 if (! isscalar (a) || ! isscalar (b))
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37 [retval, x, a, b] = common_size (x, a, b);
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38 if (retval > 0)
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39 error ("betapdf: X, A, and B must be of common size or scalars");
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40 endif
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41 endif
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42
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43 if (iscomplex (x) || iscomplex (a) || iscomplex (b))
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44 error ("betapdf: X, A, and B must not be complex");
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45 endif
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46
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47 if (isa (x, "single") || isa (a, "single") || isa (b, "single"));
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48 pdf = zeros (size (x), "single");
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49 else
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50 pdf = zeros (size (x));
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51 endif
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52
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53 k = !(a > 0) | !(b > 0) | isnan (x);
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54 pdf(k) = NaN;
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55
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56 k = (x > 0) & (x < 1) & (a > 0) & (b > 0) & ((a != 1) | (b != 1));
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57 if (isscalar (a) && isscalar (b))
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58 pdf(k) = exp ((a - 1) * log (x(k))
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59 + (b - 1) * log (1 - x(k))
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60 + gammaln (a + b) - gammaln (a) - gammaln (b));
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61 else
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62 pdf(k) = exp ((a(k) - 1) .* log (x(k))
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63 + (b(k) - 1) .* log (1 - x(k))
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64 + gammaln (a(k) + b(k)) - gammaln (a(k)) - gammaln (b(k)));
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65 endif
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66
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67 ## Most important special cases when the density is finite.
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68 k = (x == 0) & (a == 1) & (b > 0) & (b != 1);
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69 if (isscalar (a) && isscalar (b))
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70 pdf(k) = exp (gammaln (a + b) - gammaln (a) - gammaln (b));
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71 else
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72 pdf(k) = exp (gammaln (a(k) + b(k)) - gammaln (a(k)) - gammaln (b(k)));
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73 endif
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74
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75 k = (x == 1) & (b == 1) & (a > 0) & (a != 1);
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76 if (isscalar (a) && isscalar (b))
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77 pdf(k) = exp (gammaln (a + b) - gammaln (a) - gammaln (b));
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78 else
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79 pdf(k) = exp (gammaln (a(k) + b(k)) - gammaln (a(k)) - gammaln (b(k)));
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80 endif
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81
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82 k = (x >= 0) & (x <= 1) & (a == 1) & (b == 1);
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83 pdf(k) = 1;
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84
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85 ## Other special case when the density at the boundary is infinite.
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86 k = (x == 0) & (a < 1);
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87 pdf(k) = Inf;
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88
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89 k = (x == 1) & (b < 1);
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90 pdf(k) = Inf;
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91
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92 endfunction
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93
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94
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95 %!shared x,y
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96 %! x = [-1 0 0.5 1 2];
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97 %! y = [0 2 1 0 0];
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98 %!assert (betapdf (x, ones (1,5), 2*ones (1,5)), y)
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99 %!assert (betapdf (x, 1, 2*ones (1,5)), y)
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100 %!assert (betapdf (x, ones (1,5), 2), y)
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101 %!assert (betapdf (x, [0 NaN 1 1 1], 2), [NaN NaN y(3:5)])
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102 %!assert (betapdf (x, 1, 2*[0 NaN 1 1 1]), [NaN NaN y(3:5)])
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103 %!assert (betapdf ([x, NaN], 1, 2), [y, NaN])
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104
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105 ## Test class of input preserved
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106 %!assert (betapdf (single ([x, NaN]), 1, 2), single ([y, NaN]))
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107 %!assert (betapdf ([x, NaN], single (1), 2), single ([y, NaN]))
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108 %!assert (betapdf ([x, NaN], 1, single (2)), single ([y, NaN]))
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109
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110 ## Beta (1/2,1/2) == arcsine distribution
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111 %!test
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112 %! x = rand (10,1);
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113 %! y = 1./(pi * sqrt (x.*(1-x)));
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114 %! assert (betapdf (x, 1/2, 1/2), y, 50*eps);
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115
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116 ## Test large input values to betapdf
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117 %!assert (betapdf (0.5, 1000, 1000), 35.678, 1e-3)
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118
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119 ## Test input validation
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120 %!error betapdf ()
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121 %!error betapdf (1)
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122 %!error betapdf (1,2)
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123 %!error betapdf (1,2,3,4)
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124 %!error betapdf (ones (3), ones (2), ones (2))
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125 %!error betapdf (ones (2), ones (3), ones (2))
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126 %!error betapdf (ones (2), ones (2), ones (3))
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127 %!error betapdf (i, 2, 2)
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128 %!error betapdf (2, i, 2)
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129 %!error betapdf (2, 2, i)
19b9f17d22af Overhaul of statistical distribution functions
Rik <octave@nomad.inbox5.com>
parents: 11587
diff changeset
130