/usr/share/octave/packages/statistics-1.3.0/mnpdf.m is in octave-statistics 1.3.0-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 | ## Copyright (C) 2012 Arno Onken
##
## This program 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.
##
## This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{y} =} mnpdf (@var{x}, @var{p})
## Compute the probability density function of the multinomial distribution.
##
## @subheading Arguments
##
## @itemize @bullet
## @item
## @var{x} is vector with a single sample of a multinomial distribution with
## parameter @var{p} or a matrix of random samples from multinomial
## distributions. In the latter case, each row of @var{x} is a sample from a
## multinomial distribution with the corresponding row of @var{p} being its
## parameter.
##
## @item
## @var{p} is a vector with the probabilities of the categories or a matrix
## with each row containing the probabilities of a multinomial sample.
## @end itemize
##
## @subheading Return values
##
## @itemize @bullet
## @item
## @var{y} is a vector of probabilites of the random samples @var{x} from the
## multinomial distribution with corresponding parameter @var{p}. The parameter
## @var{n} of the multinomial distribution is the sum of the elements of each
## row of @var{x}. The length of @var{y} is the number of columns of @var{x}.
## If a row of @var{p} does not sum to @code{1}, then the corresponding element
## of @var{y} will be @code{NaN}.
## @end itemize
##
## @subheading Examples
##
## @example
## @group
## x = [1, 4, 2];
## p = [0.2, 0.5, 0.3];
## y = mnpdf (x, p);
## @end group
##
## @group
## x = [1, 4, 2; 1, 0, 9];
## p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8];
## y = mnpdf (x, p);
## @end group
## @end example
##
## @subheading References
##
## @enumerate
## @item
## Wendy L. Martinez and Angel R. Martinez. @cite{Computational Statistics
## Handbook with MATLAB}. Appendix E, pages 547-557, Chapman & Hall/CRC, 2001.
##
## @item
## Merran Evans, Nicholas Hastings and Brian Peacock. @cite{Statistical
## Distributions}. pages 134-136, Wiley, New York, third edition, 2000.
## @end enumerate
## @end deftypefn
## Author: Arno Onken <asnelt@asnelt.org>
## Description: PDF of the multinomial distribution
function y = mnpdf (x, p)
# Check arguments
if (nargin != 2)
print_usage ();
endif
if (! ismatrix (x) || any (x(:) < 0 | round (x(:) != x(:))))
error ("mnpdf: x must be a matrix of non-negative integer values");
endif
if (! ismatrix (p) || any (p(:) < 0))
error ("mnpdf: p must be a non-empty matrix with rows of probabilities");
endif
# Adjust input sizes
if (! isvector (x) || ! isvector (p))
if (isvector (x))
x = x(:)';
endif
if (isvector (p))
p = p(:)';
endif
if (size (x, 1) == 1 && size (p, 1) > 1)
x = repmat (x, size (p, 1), 1);
elseif (size (x, 1) > 1 && size (p, 1) == 1)
p = repmat (p, size (x, 1), 1);
endif
endif
# Continue argument check
if (any (size (x) != size (p)))
error ("mnpdf: x and p must have compatible sizes");
endif
# Count total number of elements of each multinomial sample
n = sum (x, 2);
# Compute probability density function of the multinomial distribution
t = x .* log (p);
t(x == 0) = 0;
y = exp (gammaln (n+1) - sum (gammaln (x+1), 2) + sum (t, 2));
# Set invalid rows to NaN
k = (abs (sum (p, 2) - 1) > 1e-6);
y(k) = NaN;
endfunction
%!test
%! x = [1, 4, 2];
%! p = [0.2, 0.5, 0.3];
%! y = mnpdf (x, p);
%! assert (y, 0.11812, 0.001);
%!test
%! x = [1, 4, 2; 1, 0, 9];
%! p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8];
%! y = mnpdf (x, p);
%! assert (y, [0.11812; 0.13422], 0.001);
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