--- /dev/null
+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## This file is part of Octave.
+##
+## Octave 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.
+##
+## Octave 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 Octave; see the file COPYING. If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} moment (@var{x}, @var{p})
+## @deftypefnx {Function File} {} moment (@var{x}, @var{p}, @var{type})
+## @deftypefnx {Function File} {} moment (@var{x}, @var{p}, @var{dim})
+## @deftypefnx {Function File} {} moment (@var{x}, @var{p}, @var{type}, @var{dim})
+## @deftypefnx {Function File} {} moment (@var{x}, @var{p}, @var{dim}, @var{type})
+## Compute the @var{p}-th moment of the vector @var{x} about zero.
+## @tex
+## $$
+## {\rm moment} (x) = { \sum_{i=1}^N {x_i}^p \over N }
+## $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+## moment (x) = 1/N SUM_i x(i)^p
+## @end group
+## @end example
+##
+## @end ifnottex
+##
+## If @var{x} is a matrix, return the row vector containing the
+## @var{p}-th moment of each column.
+##
+## The optional string @var{type} specifies the type of moment to be computed.
+## Valid options are:
+##
+## @table @asis
+## @item "c"
+## Central Moment. The moment about the mean defined as
+## @tex
+## $$
+## {\sum_{i=1}^N (x_i - \bar{x})^p \over N}
+## $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+## 1/N SUM_i (x(i) - mean(x))^p
+## @end group
+## @end example
+##
+## @end ifnottex
+##
+## @item "a"
+## Absolute Moment. The moment about zero ignoring sign defined as
+## @tex
+## $$
+## {\sum_{i=1}^N {\left| x_i \right|}^p \over N}
+## $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+## 1/N SUM_i ( abs (x(i)) )^p
+## @end group
+## @end example
+##
+## @end ifnottex
+##
+## @item "ac"
+## Absolute Central Moment. Defined as
+## @tex
+## $$
+## {\sum_{i=1}^N {\left| x_i - \bar{x} \right|}^p \over N}
+## $$
+## @end tex
+## @ifnottex
+##
+## @example
+## @group
+## 1/N SUM_i ( abs (x(i) - mean(x)) )^p
+## @end group
+## @end example
+##
+## @end ifnottex
+## @end table
+##
+## If the optional argument @var{dim} is given, operate along this dimension.
+##
+## If both @var{type} and @var{dim} are given they may appear in any order.
+## @seealso{var, skewness, kurtosis}
+## @end deftypefn
+
+## Can easily be made to work for continuous distributions (using quad)
+## as well, but how does the general case work?
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: Compute moments
+
+function m = moment (x, p, opt1, opt2)
+
+ if (nargin < 2 || nargin > 4)
+ print_usage ();
+ endif
+
+ if (!(isnumeric (x) || islogical (x)) || isempty (x))
+ error ("moment: X must be a non-empty numeric matrix or vector");
+ endif
+
+ if (! (isnumeric (p) && isscalar (p)))
+ error ("moment: P must be a numeric scalar");
+ endif
+
+ need_dim = false;
+
+ if (nargin == 2)
+ type = "";
+ need_dim = true;
+ elseif (nargin == 3)
+ if (ischar (opt1))
+ type = opt1;
+ need_dim = true;
+ else
+ dim = opt1;
+ type = "";
+ endif
+ elseif (nargin == 4)
+ if (ischar (opt1))
+ type = opt1;
+ dim = opt2;
+ elseif (ischar (opt2))
+ type = opt2;
+ dim = opt1;
+ else
+ error ("moment: expecting TYPE to be a string");
+ endif
+ endif
+
+ nd = ndims (x);
+ sz = size (x);
+ if (need_dim)
+ ## Find the first non-singleton dimension.
+ (dim = find (sz > 1, 1)) || (dim = 1);
+ else
+ if (!(isscalar (dim) && dim == fix (dim)) ||
+ !(1 <= dim && dim <= nd))
+ error ("moment: DIM must be an integer and a valid dimension");
+ endif
+ endif
+
+ n = sz(dim);
+
+ if (any (type == "c"))
+ x = center (x, dim);
+ endif
+ if any (type == "a")
+ x = abs (x);
+ endif
+
+ m = sum (x .^ p, dim) / n;
+
+endfunction
+
+
+%!test
+%! x = rand (10);
+%! assert (moment (x,1), mean (x), 1e1*eps);
+%! assert (moment (x,2), meansq (x), 1e1*eps);
+%! assert (moment (x,1,2), mean (x,2), 1e1*eps);
+%! assert (moment (x,1,'c'), mean (center (x)), 1e1*eps);
+%! assert (moment (x,1,'a'), mean (abs (x)), 1e1*eps);
+
+%!assert (moment (single([1 2 3]),1), single(2));
+
+%% Test input validation
+%!error moment ()
+%!error moment (1)
+%!error moment (1, 2, 3, 4, 5)
+%!error moment (['A'; 'B'], 2)
+%!error moment (ones(2,0,3), 2)
+%!error moment (1, true)
+%!error moment (1, ones(2,2))
+%!error moment (1, 2, 3, 4)
+%!error moment (1, 2, ones(2,2))
+%!error moment (1, 2, 1.5)
+%!error moment (1, 2, 4)
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff