moment.m

GNU Octave is a high-level language, primarily intended for numerical computations. It provides a c

## Copyright (C) 1995, 1996, 1997  Kurt Hornik
## 
## 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 2, 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 file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## usage:  moment (x, p [, opt])
##
## Computes the p-th moment of x if it is a vector;  if x is a matrix,
## return the row vector of the p-th moment of each column.
##
## With the optional string opt, the kind of moment to be computed can
## be specified.  If opt contains `c' or `a', central and/or absolute
## moments are returned.  I.e., `moment(x, 3, "ac")' computes the third
## central absolute moment of x.

## Can easily be made to work for continuous distributions (using quad)
## as well, but how does the general case work?
  
## Author:  KH <[e-mail]>
## Description:  Compute moments
  
function m = moment (x, p, opt)
  
  if ((nargin < 2) || (nargin > 3))
    usage ("moment (x, p [, type]")
  endif
  
  [nr, nc] = size (x);
  if (nr == 0 || nc == 0)
    error ("moment:  x must not be empty");
  elseif (nr == 1)
    x  = reshape (x, nc, 1);
    nr = nc;
  endif
  
  if (nargin == 3)
    tmp = implicit_str_to_num_ok;
    implicit_str_to_num_ok = "true";
    if any (opt == "c")
      x = x - ones (nr, 1) * sum (x) / nr;
    endif
    if any (opt == "a")
      x = abs (x);
    endif
    implicit_str_to_num_ok = tmp;
  endif
  
  m = sum(x .^ p) / nr;
  
endfunction