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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 .
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{x} =} mnrnd (@var{n}, @var{p})
+## @deftypefnx {Function File} {@var{x} =} mnrnd (@var{n}, @var{p}, @var{s})
+## Generate random samples from the multinomial distribution.
+##
+## @subheading Arguments
+##
+## @itemize @bullet
+## @item
+## @var{n} is the first parameter of the multinomial distribution. @var{n} can
+## be scalar or a vector containing the number of trials of each multinomial
+## sample. The elements of @var{n} must be non-negative integers.
+##
+## @item
+## @var{p} is the second parameter of the multinomial distribution. @var{p} can
+## be a vector with the probabilities of the categories or a matrix with each
+## row containing the probabilities of a multinomial sample. If @var{p} has
+## more than one row and @var{n} is non-scalar, then the number of rows of
+## @var{p} must match the number of elements of @var{n}.
+##
+## @item
+## @var{s} is the number of multinomial samples to be generated. @var{s} must
+## be a non-negative integer. If @var{s} is specified, then @var{n} must be
+## scalar and @var{p} must be a vector.
+## @end itemize
+##
+## @subheading Return values
+##
+## @itemize @bullet
+## @item
+## @var{x} is a matrix of random samples from the multinomial distribution with
+## corresponding parameters @var{n} and @var{p}. Each row corresponds to one
+## multinomial sample. The number of columns, therefore, corresponds to the
+## number of columns of @var{p}. If @var{s} is not specified, then the number
+## of rows of @var{x} is the maximum of the number of elements of @var{n} and
+## the number of rows of @var{p}. If a row of @var{p} does not sum to @code{1},
+## then the corresponding row of @var{x} will contain only @code{NaN} values.
+## @end itemize
+##
+## @subheading Examples
+##
+## @example
+## @group
+## n = 10;
+## p = [0.2, 0.5, 0.3];
+## x = mnrnd (n, p);
+## @end group
+##
+## @group
+## n = 10 * ones (3, 1);
+## p = [0.2, 0.5, 0.3];
+## x = mnrnd (n, p);
+## @end group
+##
+## @group
+## n = (1:2)';
+## p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8];
+## x = mnrnd (n, 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
+## Description: Random samples from the multinomial distribution
+
+function x = mnrnd (n, p, s)
+
+ # Check arguments
+ if (nargin == 3)
+ if (! isscalar (n) || n < 0 || round (n) != n)
+ error ("mnrnd: n must be a non-negative integer");
+ endif
+ if (! isvector (p) || any (p < 0 | p > 1))
+ error ("mnrnd: p must be a vector of probabilities");
+ endif
+ if (! isscalar (s) || s < 0 || round (s) != s)
+ error ("mnrnd: s must be a non-negative integer");
+ endif
+ elseif (nargin == 2)
+ if (isvector (p) && size (p, 1) > 1)
+ p = p';
+ endif
+ if (! isvector (n) || any (n < 0 | round (n) != n) || size (n, 2) > 1)
+ error ("mnrnd: n must be a non-negative integer column vector");
+ endif
+ if (! ismatrix (p) || isempty (p) || any (p < 0 | p > 1))
+ error ("mnrnd: p must be a non-empty matrix with rows of probabilities");
+ endif
+ if (! isscalar (n) && size (p, 1) > 1 && length (n) != size (p, 1))
+ error ("mnrnd: the length of n must match the number of rows of p");
+ endif
+ else
+ print_usage ();
+ endif
+
+ # Adjust input sizes
+ if (nargin == 3)
+ n = n * ones (s, 1);
+ p = repmat (p(:)', s, 1);
+ elseif (nargin == 2)
+ if (isscalar (n) && size (p, 1) > 1)
+ n = n * ones (size (p, 1), 1);
+ elseif (size (p, 1) == 1)
+ p = repmat (p, length (n), 1);
+ endif
+ endif
+ sz = size (p);
+
+ # Upper bounds of categories
+ ub = cumsum (p, 2);
+ # Make sure that the greatest upper bound is 1
+ gub = ub(:, end);
+ ub(:, end) = 1;
+ # Lower bounds of categories
+ lb = [zeros(sz(1), 1) ub(:, 1:(end-1))];
+
+ # Draw multinomial samples
+ x = zeros (sz);
+ for i = 1:sz(1)
+ # Draw uniform random numbers
+ r = repmat (rand (n(i), 1), 1, sz(2));
+ # Compare the random numbers of r to the cumulated probabilities of p and
+ # count the number of samples for each category
+ x(i, :) = sum (r <= repmat (ub(i, :), n(i), 1) & r > repmat (lb(i, :), n(i), 1), 1);
+ endfor
+ # Set invalid rows to NaN
+ k = (abs (gub - 1) > 1e-6);
+ x(k, :) = NaN;
+
+endfunction
+
+%!test
+%! n = 10;
+%! p = [0.2, 0.5, 0.3];
+%! x = mnrnd (n, p);
+%! assert (size (x), size (p));
+%! assert (all (x >= 0));
+%! assert (all (round (x) == x));
+%! assert (sum (x) == n);
+
+%!test
+%! n = 10 * ones (3, 1);
+%! p = [0.2, 0.5, 0.3];
+%! x = mnrnd (n, p);
+%! assert (size (x), [length(n), length(p)]);
+%! assert (all (x >= 0));
+%! assert (all (round (x) == x));
+%! assert (all (sum (x, 2) == n));
+
+%!test
+%! n = (1:2)';
+%! p = [0.2, 0.5, 0.3; 0.1, 0.1, 0.8];
+%! x = mnrnd (n, p);
+%! assert (size (x), size (p));
+%! assert (all (x >= 0));
+%! assert (all (round (x) == x));
+%! assert (all (sum (x, 2) == n));