/usr/share/octave/packages/nan-3.1.4/statistic.m is in octave-nan 3.1.4-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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% STATISTIC estimates various statistics at once.
%
% R = STATISTIC(x,DIM)
% calculates all statistic (see list of fun) in dimension DIM
% R is a struct with all statistics
%
% y = STATISTIC(x,fun)
% estimate of fun on dimension DIM
% y gives the statistic of fun
%
% DIM dimension
% 1: STATS of columns
% 2: STATS of rows
% N: STATS of N-th dimension
% default or []: first DIMENSION, with more than 1 element
%
% fun 'mean' mean
% 'std' standard deviation
% 'var' variance
% 'sem' standard error of the mean
% 'rms' root mean square
% 'meansq' mean of squares
% 'sum' sum
% 'sumsq' sum of squares
% 'CM#' central moment of order #
% 'skewness' skewness
% 'kurtosis' excess coefficient (Fisher kurtosis)
% 'mad' mean absolute deviation
%
% features:
% - can deal with NaN's (missing values)
% - dimension argument
% - compatible to Matlab and Octave
%
% see also: SUMSKIPNAN
%
% REFERENCE(S):
% [1] http://www.itl.nist.gov/
% [2] http://mathworld.wolfram.com/
% $Id$
% Copyright (C) 2000-2003,2010 by Alois Schloegl <alois.schloegl@gmail.com>
% This function is part of the NaN-toolbox
% http://pub.ist.ac.at/~schloegl/matlab/NaN/
% 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; If not, see <http://www.gnu.org/licenses/>.
if nargin==1,
DIM=[];
fun=[];
elseif nargin==2,
if ~isnumeric(DIM),
fun=DIM;
DIM=[];
else
fun=[];
end
end
if isempty(DIM),
DIM = find(size(i)>1,1);
if isempty(DIM), DIM=1; end;
end;
%R.N = sumskipnan(~isnan(i),DIM); % number of elements
[R.SUM,R.N,R.SSQ] = sumskipnan(i,DIM); % sum
%R.S3P = sumskipnan(i.^3,DIM); % sum of 3rd power
R.S4P = sumskipnan(i.^4,DIM); % sum of 4th power
%R.S5P = sumskipnan(i.^5,DIM); % sum of 5th power
R.MEAN = R.SUM./R.N; % mean
R.MSQ = R.SSQ./R.N; % mean square
R.RMS = sqrt(R.MSQ); % root mean square
%R.SSQ0 = R.SSQ-R.SUM.*R.MEAN; % sum square of mean removed
R.SSQ0 = R.SSQ - real(R.SUM).*real(R.MEAN) - imag(R.SUM).*imag(R.MEAN); % sum square of mean removed
%if flag_implicit_unbiased_estim; %% ------- unbiased estimates -----------
n1 = max(R.N-1,0); % in case of n=0 and n=1, the (biased) variance, STD and SEM are INF
%else
% n1 = R.N;
%end;
R.VAR = R.SSQ0./n1; % variance (unbiased)
R.STD = sqrt(R.VAR); % standard deviation
R.SEM = sqrt(R.SSQ0./(R.N.*n1)); % standard error of the mean
R.SEV = sqrt(n1.*(n1.*R.S4P./R.N+(R.N.^2-2*R.N+3).*(R.SSQ./R.N).^2)./(R.N.^3)); % standard error of the variance
R.COEFFICIENT_OF_VARIATION = R.STD./R.MEAN;
q = quantile(i, (1:3)/4, DIM);
%sz=size(i);sz(DIM)=1;
%Q0500=repmat(nan,sz);
%Q0250=Q0500;
%Q0750=Q0500;
%MODE=Q0500;
%for k=1:size(i,2),
% tmp = sort(i(:,k));
%ix = find(~~diff([-inf;tmp;inf]))
%ix2=diff(ix)
%MODE(k)= tmp(max(ix2)==ix2)
% Q0500(k) = flix(tmp,R.N(k)/2 + 0.5);
% Q0250(k) = flix(tmp,R.N(k)/4 + 0.5);
% Q0750(k) = flix(tmp,R.N(k)*3/4 + 0.5);
%end;
%R.MEDIAN = Q0500;
%R.Quartiles = [Q0250; Q0750];
%R.Skewness.Fisher = (R.CM3)./(R.STD.^3); %%% same as R.SKEWNESS
%R.Skewness.Pearson_Mode = (R.MEAN-R.MODE)./R.STD;
%R.Skewness.Pearson_coeff1 = (3*R.MEAN-R.MODE)./R.STD;
%R.Skewness.Pearson_coeff2 = (3*R.MEAN-R.MEDIAN)./R.STD;
%R.Skewness.Bowley = (Q0750+Q0250 - 2*Q0500)./(Q0750-Q0250); % quartile skewness coefficient
R.CM2 = R.SSQ0./n1;
szi = size(i); szm = [size(R.MEAN),1];
i = i - repmat(R.MEAN,szi./szm(1:length(szi)));
R.CM3 = sumskipnan(i.^3,DIM)./n1;
R.CM4 = sumskipnan(i.^4,DIM)./n1;
%R.CM5 = sumskipnan(i.^5,DIM)./n1;
R.SKEWNESS = R.CM3./(R.STD.^3);
R.KURTOSIS = R.CM4./(R.VAR.^2)-3;
[R.MAD,N] = sumskipnan(abs(i),DIM); % mean absolute deviation
R.MAD = R.MAD./n1;
R.datatype = 'STAT Level 3';
tmp = version;
if 0, %str2num(tmp(1))*1000+str2num(tmp(3))*100+str2num(tmp(5:6))<2136,
% ###obsolete: was needed for Octave version < 2.1.36
if strcmp(fun(1:2),'CM')
oo = str2double(fun(3:length(fun)));
varargout = sumskipnan(i.^oo,DIM)./n1;
elseif isempty(fun)
varargout = R;
else
varargout = getfield(R,upper(fun));
end;
else
if iscell(fun),
for k=1:length(fun),
if strcmp(fun{k}(1:2),'CM')
oo = str2double(fun{k}(3:length(fun{k})));
varargout{k} = sumskipnan(i.^oo,DIM)./n1;
else
varargout{k} = getfield(R,upper(fun{k}));
end;
end;
elseif ischar(fun),
if strcmp(fun(1:2),'CM')
oo = str2double(fun(3:length(fun)));
varargout{1} = sumskipnan(i.^oo,DIM)./n1;
else
varargout{1} = getfield(R,upper(fun));
end;
else
varargout{1} = R;
end;
end;
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