Logo Search packages:      
Sourcecode: octave-nan version File versions  Download package

std.m

function [o,v]=std(x,opt,DIM)
% STD calculates the standard deviation.
% 
% [y,v] = std(x [, opt[, DIM]])
% 
% opt   option 
%     0:  normalizes with N-1 [default]
%           provides the square root of best unbiased estimator of the variance
%     1:  normalizes with N, 
%           this provides the square root of the second moment around the mean
%     otherwise: 
%               best unbiased estimator of the standard deviation (see [1])      
%
% DIM dimension
%     N STD of  N-th dimension 
%     default or []: first DIMENSION, with more than 1 element
%
% y   estimated standard deviation
%
% features:
% - provides an unbiased estimation of the S.D. 
% - can deal with NaN's (missing values)
% - dimension argument also in Octave
% - compatible to Matlab and Octave
%
% see also: RMS, SUMSKIPNAN, MEAN, VAR, MEANSQ,
%
%
% References(s):
% [1] http://mathworld.wolfram.com/StandardDeviationDistribution.html


%    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 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 <http://www.gnu.org/licenses/>.

%     $Revision: 4585 $
%     $Id: std.m 4585 2008-02-04 13:47:45Z adb014 $
%     Copyright (C) 2000-2003, 2006 by Alois Schloegl <a.schloegl@ieee.org>   
%       This is part of the NaN-toolbox for Octave and Matlab 
%       see also: http://hci.tugraz.at/schloegl/matlab/NaN/       

if nargin<3,
      DIM = []; 
end;
if isempty(DIM), 
        DIM=min(find(size(x)>1));
        if isempty(DIM), DIM=1; end;
end;

[y,n] = sumskipnan(center(x,DIM).^2,DIM);

if nargin<2,
        opt = 0;
end;

if opt==0, 
        % square root if the best unbiased estimator of the variance 
        ib = inf;
        o  = sqrt(y./max(n-1,0));   % normalize
        
elseif opt==1, 
      ib = NaN;        
        o  = sqrt(y./n);

else
        % best unbiased estimator of the mean
        if exist('unique')==2, 
            % usually only a few n's differ
                [N,tmp,tix] = unique(n(:));     % compress n and calculate ib(n)
            ib = sqrt(N/2).*gamma((N-1)./2)./gamma(N./2);   %inverse b(n) [1]
              ib = ib(reshape(tix,size(y)));    % expand ib to correct size
                
        elseif exist('histo3')==2, 
            % usually only a few n's differ
                [N,tix] = histo3(n(:)); N = N.X;
                ib = sqrt(N/2).*gamma((N-1)./2)./gamma(N./2);     %inverse b(n) 
              ib = ib(reshape(tix,size(y)));    % expand ib to correct size
                
        else      % gamma is called prod(size(n)) times 
                ib = sqrt(n/2).*gamma((n-1)./2)./gamma(n./2);     %inverse b(n) [1]
        end;      
        o  = sqrt(y./n).*ib;
end;

if nargout>1,
      v = y.*((max(n-1,0)./(n.*n))-1./(n.*ib.*ib)); % variance of the estimated S.D. ??? needs further checks
end;



Generated by  Doxygen 1.6.0   Back to index