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+## 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);