--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/m-toolbox/classes/+utils/@math/KSpValue.m	Wed Nov 23 19:22:13 2011 +0100
@@ -0,0 +1,86 @@
+% KSpValue Compute p-Value of the Kolmogorov - Smirnov distribution
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% Compute p-Value of the Kolmogorov - Smirnov distribution
+%
+% CALL
+%
+% pValue = utils.math.KSpValue(KSstatistic,n1,n2);
+%
+%
+% INPUT
+%
+% - KSstatistic, value of the statistic of the KS distribution.
+% Corresponding at KSstatistic = max(abs(CD1-CD2))
+% - length of the first data series
+% - length of the second data series
+%
+% References:
+%   Marsaglia, G., W.W. Tsang, and J. Wang (2003), "Evaluating Kolmogorov`s
+%         Distribution", Journal of Statistical Software, vol. 8, issue 18.
+%
+%
+% L Ferraioli 06-12-2010
+%
+% $Id: KSpValue.m,v 1.3 2011/07/14 07:10:16 mauro Exp $
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function pValue = KSpValue(KSstatistic, n1, n2)
+  
+  if isempty(n2)
+    n = n1; % test against theoretical distribution
+  else
+    n = n1*n2/(n1+n2); % test of two empirical distributions
+  end
+  s = n*KSstatistic^2;
+  
+  % Following the recipe described in described in Marsaglia, et al.
+  % For d values that are in the far tail of the distribution (i.e.
+  % p-values > .999), the following lines will speed up the computation
+  % significantly, and provide accuracy up to 7 digits.
+  if s == 0
+    pValue = 0;
+  else
+    if (s > 7.24) || ((s > 3.76) && (n > 99))
+      pValue = 2*exp(-(2.000071+.331/sqrt(n)+1.409/n)*s);
+    else
+      % Express d as d = (k-h)/n, where k is a +ve integer and 0 < h < 1.
+      k = ceil(KSstatistic*n);
+      h = k - KSstatistic*n;
+      m = 2*k-1;
+      
+      % Create the H matrix, which describes the CDF, as described in Marsaglia,
+      % et al.
+      if m > 1
+        c = 1./gamma((1:m)' + 1);
+        
+        r = zeros(1,m);
+        r(1) = 1;
+        r(2) = 1;
+        
+        T = toeplitz(c,r);
+        
+        T(:,1) = T(:,1) - (h.^[1:m]')./gamma((1:m)' + 1);
+        
+        T(m,:) = fliplr(T(:,1)');
+        T(m,1) = (1 - 2*h^m + max(0,2*h-1)^m)/gamma(m+1);
+      else
+        T = (1 - 2*h^m + max(0,2*h-1)^m)/gamma(m+1);
+      end
+      
+      % Scaling before raising the matrix to a power
+      if ~isscalar(T)
+        lmax = max(eig(T));
+        T = (T./lmax)^n;
+      else
+        lmax = 1;
+      end
+      
+      % Pr(Dn < d) = n!/n * tkk ,  where tkk is the kth element of Tn = T^n.
+      % p-value = Pr(Dn > d) = 1-Pr(Dn < d)
+      pValue = (1 - exp(gammaln(n+1) + n*log(lmax) - n*log(n)) * T(k,k));
+    end
+  end
+  pValue = abs(pValue);
+  
+end