## Copyright (C) 1995-2017 Friedrich Leisch
##
## This file is part of the statistics package for GNU Octave.
##
##
## 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; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn  {statistics} @var{r} = wienrnd (@var{t}, @var{d}, @var{n})
##
## Return a simulated realization of the @var{d}-dimensional Wiener Process
## on the interval [0, @var{t}].
##
## If @var{d} is omitted, @var{d} = 1 is used.  The first column of the
## return matrix contains time, the remaining columns contain the Wiener
## process.
##
## The optional parameter @var{n} defines the number of summands used for
## simulating the process over an interval of length 1.  If @var{n} is
## omitted, @var{n} = 1000 is used.
## @end deftypefn

function r = wienrnd (t, d, n)

  if (nargin == 1)
    d = 1;
    n = 1000;
  elseif (nargin == 2)
    n = 1000;
  elseif (nargin > 3)
    print_usage ();
  endif

  if (! isscalar (t) || ! isscalar (d) || ! isscalar (n))
    error ("wienrnd: T, D, and N must all be positive integers.");
  endif

  r = randn (n * t, d);
  r = cumsum (r) / sqrt (n);

  r = [((1: n*t)' / n), r];

endfunction
