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scripts/statistics/base/moment.m

changeset 10289: 4b124317dc38
parent:93c65f2a5668
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (71 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2003, 2004, 2005,

     2##               2006, 2007 Kurt Hornik

     3##

     4## This file is part of Octave.

     5##

     6## Octave is free software; you can redistribute it and/or modify it

     7## under the terms of the GNU General Public License as published by

     8## the Free Software Foundation; either version 3 of the License, or (at

     9## your option) any later version.

    10##

    11## Octave is distributed in the hope that it will be useful, but

    12## WITHOUT ANY WARRANTY; without even the implied warranty of

    13## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

    14## General Public License for more details.

    15##

    16## You should have received a copy of the GNU General Public License

    17## along with Octave; see the file COPYING.  If not, see

    18## <http://www.gnu.org/licenses/>.

    19

    20## -*- texinfo -*-

    21## @deftypefn {Function File} {} moment (@var{x}, @var{p}, @var{opt}, @var{dim})

    22## If @var{x} is a vector, compute the @var{p}-th moment of @var{x}.

    23##

    24## If @var{x} is a matrix, return the row vector containing the

    25## @var{p}-th moment of each column.

    26##

    27## With the optional string opt, the kind of moment to be computed can

    28## be specified.  If opt contains @code{"c"} or @code{"a"}, central

    29## and/or absolute moments are returned.  For example,

    30##

    31## @example

    32## moment (x, 3, "ac")

    33## @end example

    34##

    35## @noindent

    36## computes the third central absolute moment of @var{x}.

    37##

    38## If the optional argument @var{dim} is supplied, work along dimension

    39## @var{dim}.

    40## @end deftypefn

    41

    42## Can easily be made to work for continuous distributions (using quad)

    43## as well, but how does the general case work?

    44

    45## Author: KH <Kurt.Hornik@wu-wien.ac.at>

    46## Description: Compute moments

    47

    48function m = moment (x, p, opt1, opt2)

    49

    50  if ((nargin < 2) || (nargin > 4))

    51    print_usage ();

    52  endif

    53

    54  need_dim = 0;

    55

    56  if (nargin == 2)

    57    opt = "";

    58    need_dim = 1;

    59  elseif (nargin == 3)

    60    if (ischar (opt1))

    61      opt = opt1;

    62      need_dim = 1;

    63    else

    64      dim = opt1;

    65      opt = "";

    66    endif

    67  elseif (nargin == 4)

    68    if (ischar (opt1))

    69      opt = opt1;

    70      dim = opt2;

    71    elseif (ischar (opt2))

    72      opt = opt2;

    73      dim = opt1;

    74    else

    75      error ("moment: expecting opt to be a string");

    76    endif

    77  else

    78    print_usage ();

    79  endif

    80

    81  if (need_dim)

    82    t = find (size (x) != 1);

    83    if (isempty (t))

    84      dim = 1;

    85    else

    86      dim = t(1);

    87    endif

    88  endif

    89

    90  sz = size (x);

    91  n = sz (dim);

    92

    93  if (numel (x) < 1)

    94    error ("moment: x must not be empty");

    95  endif

    96

    97  if any (opt == "c")

    98    rng = ones (1, length (sz));

    99    rng(dim) = sz(dim);

   100    x = x - repmat (sum (x, dim), rng) / n;

   101  endif

   102  if any (opt == "a")

   103    x = abs (x);

   104  endif

   105

   106  m = sum (x .^ p, dim) / n;

   107

   108endfunction