TLim (nrsamp, lv, confidence)

%Function TLim
%
%TLim calculates the confidence limit for Hotelling T values of a
%principal components decomposition. Samples with a T value above this
%confidence limit are considered to be multivariate outliers.
%
%Syntax:
%    limit = TLim (nrsamp, lv, confidence)
%
%Input parameters:
%    nrsamp: the number of samples in the dataset
%    lv: the number of latent variables that is used for the principal
%        components analysis
%    confidence: the confidence level (must be between 0 and 1), default: 0.95 
%
%Output parameters:
%    limit: the confidence limit for Hotelling T values
%
%Example:
%    limit = TLim (100, 6, 0.95); %confidence limit for a dataset of 100 samples and 6 PC's
%
%Literature:
%    1) Mason RL, Chou YM and Young JC (2001). Applying Hotelling's T2
%    statistic to batch processes. Journal of Quality Technology, 33(4),
%    466-479.
%
%This function uses the finv method from the statistics toolbox to
%calculate the value for the inverse cumulative distribution function of
%the F distribution.

%The Biodata toolbox for MATLAB: a spectral database system for storing and
%processing spectra
%C 2008, Kris De Gussem, Raman Spectroscopy Research Group, Department
%of analytical chemistry, Ghent University
%C 2009 Kris De Gussem
%
%This file is part of Biodata.
%
%Biodata 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.
%
%Biodata 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 Biodata.  If not, see <http://www.gnu.org/licenses/>.

%Copyright (c) 2008-2009, Kris De Gussem
%All rights reserved.
%
%Redistribution and use in source and binary forms, with or without 
%modification, are permitted provided that the following conditions are 
%met:
%
%    * Redistributions of source code must retain the above copyright 
%      notice, this list of conditions and the following disclaimer.
%    * Redistributions in binary form must reproduce the above copyright 
%      notice, this list of conditions and the following disclaimer in 
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%    * Neither the name of Raman Spectroscopy Research Group, Department of
%	  analytical chemistry, Ghent University nor the names 
%      of its contributors may be used to endorse or promote products derived 
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%      
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function limit = TLim (nrsamp, lv, confidence)
switch nargin
    case 2
        confidence = 0.95;
    case 3
    otherwise
        error ('Biodata:msg', 'Wrong number of input arguments. See help TLim for more information.');
end

if ~((0<confidence) && (confidence<1))
    error ('Biodata:msg', 'Confidence limit must be between 0 and 1.');
end

if lv >= nrsamp
    warning ('Biodata:msg', 'Confidence limit can not be calculated if the number of latent variables is equal to or higher than the number of samples.');
    limit = NaN; %not a number
else
    try
        %use the statistics toolbox function
        fvalue = finv (confidence, lv, nrsamp-lv);
    catch
        %if we do not have the statistics toolbox, then try the
        %corresponding function in the PLS toolbox
        fvalue = ftest (1 - confidence, lv, nrsamp-lv);
    end
    limit = (lv * (nrsamp-1)) / (nrsamp-lv) * fvalue;
end