%#									    
%# function [ks,kscrit]=kolmog(x,alpha);				    
%#									    
%# AIM:		Kolmogorov-Smirnov test to check if a set of observations are  
%#		normally distributed.					
%#									   
%# PRINCIPLE:	The test consists in determining the largest difference between
%#		two cumulative relative frequency distributions: the observed
%#		distribution and the expected (normal) distribution. The test 
%#		is only applicable to continuous distributions.		
%#								
%# REFERENCE:   "Handbook of Chemometrics and Qualimetrics, Part A"
%#		Massart, Vandeginste, Buydens, De Jong, Lewi, Smeyers-Verbeke
%#		Elsevier, 1997, p.117.				
%#									     
%# INPUT:	x: 	Vector of observations (row- or column-vector).     	
%#  		alpha	Critical level to apply the test (0.1, 0.05 or 0.01).  
%#			Ex: alpha=0.05 --> Test at the 5% level		
%#									   	 
%# OUTPUT:	ks:	The calculated value for the test.		
%#		kscrit:	The tabulated value for the test.		
%#			If ks < kscrit, the observations can be considered as
%#			normally distributed, otherwise not.	 
%#									     
%# SUBROUTINES:	pietstat.dll:	Dynamic link library containing the statistical
%#				table for the one-sided normal test.
%#		kolsmir.mat:	Matrix containing tabulated values for the
%#				Kolmogorov-Smirnov test.			
%#									    
%# AUTHOR:	Frederic Despagne					    
%#		Copyright (c) 1998 for ChemoAC				    
%#		Dienst FABI, Vrije Universiteit Brussels		   
%#		Laarbeeklaan 103 Jette					    
%#									    
%# VERSION: 1.1 (28/12/1998)						    
%#									    
%# TEST:								    
%#									    

function [ks,kscrit]=kolmog(x,alpha);

load kolsmir
x = sort(x);		% Observations sorted in ascending order.
if alpha == 0.1;
	col = 2;
elseif alpha == 0.05
	col = 3;
else
	col = 4;
end
[a,b] = size(x);
if min([a b]) ~= 1
	error('Observations must be input in a row- or column-vector, not in matrix')
end
n = length(x);		% Number of observations.
mx = mean(x);		% Mean of observations.
stdx = std(x);		% Standard deviation of observations.
z = (x-mx)/stdx;	% Vector of standardised deviations from the mean.
for i=1:n		% Determination of cumulative relative expected frequencies.
	if z(i) < 0
		FE(i) = pietstat(13,z(i));
	else
		FE(i) = 1-pietstat(13,z(i));
	end
	FO(i) = i/n;
end
d = abs(FO-FE);		% Differences between the two distributions.
maxd = max(d);
FOm = zeros(size(FO));
FOm(2:n) = FO(1:n-1);
dm = abs(FOm-FE);	
maxdm = max(dm);
ks = max([maxd maxdm]);	% Calculated test value.
index = find(kstable(:,1)==n);
if isempty(index)
	if col == 2
		kscrit = 0.84*sqrt(n);
	elseif col == 3
		kscrit = 0.9*sqrt(n);
	else
		kscrit = 1.05*sqrt(n);
	end
else
	kscrit = kstable(index,col);
end