npcdf

npcdf - Non-parametric cumulative distribution function.

 Given a list of samples drawn from an unknown (non-parametric) distribution,
 the corresponding cumulative distribution function is evaluated at a set of
 given points.

  USAGE

    p = npcdf(X,x)

    X              list of samples drawn from the unknown distribution
    x              set of points where the cdf should be evaluated

0001 function p = npcdf(X,x)
0002 
0003 %npcdf - Non-parametric cumulative distribution function.
0004 %
0005 % Given a list of samples drawn from an unknown (non-parametric) distribution,
0006 % the corresponding cumulative distribution function is evaluated at a set of
0007 % given points.
0008 %
0009 %  USAGE
0010 %
0011 %    p = npcdf(X,x)
0012 %
0013 %    X              list of samples drawn from the unknown distribution
0014 %    x              set of points where the cdf should be evaluated
0015 %
0016 
0017 % Copyright (C) 2010-2011 by Michaël Zugaro
0018 %
0019 % This program is free software; you can redistribute it and/or modify
0020 % it under the terms of the GNU General Public License as published by
0021 % the Free Software Foundation; either version 3 of the License, or
0022 % (at your option) any later version.
0023 
0024 if nargin < 2,
0025   error('Incorrect number of parameters (type ''help <a href="matlab:help npcdf">npcdf</a>'' for details).');
0026 end
0027 
0028 % Get rid of NaNs, reshape inputs as vectors
0029 X(isnan(X)) = [];
0030 X = X(:);
0031 nX = length(X);
0032 x(isnan(x)) = [];
0033 x = x(:);
0034 nx = length(x);
0035 
0036 % Construct a matrix where the first column is a concatenation of the samples and points,
0037 % the second is 1 for samples and 0 for points, and the third is the order of the points
0038 % (this will be necessary to keep track of the points after the matrix is reordered)
0039 Y = [X ones(nX,1) zeros(nX,1);x zeros(nx,1) (1:nx)'];
0040 % Sort samples and points in ascending order, so that the position of the points in the matrix
0041 % (row numbers) corresponds to their cdf values
0042 [Y,i] = sortrows(Y);
0043 
0044 % Actually, row numbers should only take samples into account; this is precisely what the
0045 % second column of Y is for (it has 1 for samples and 0 for points)
0046 F = cumsum(Y(:,2))/nX;
0047 % Now that we have the value of the cdf at each sample and each point, we need to extract
0048 % the value at the points; again, we use the second column of Y (it has 0 for points)
0049 tested = Y(:,2) == 0;
0050 % Because Y was reordered (sortrows), we need to reorder the values of F back to the order
0051 % in which the points were listed in x
0052 p(Y(tested,3)) = F(tested);