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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % ECDF Compute empirical cumulative distribution function
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 % Compute empirical cumulative distribution function for a series of data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % CALL
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % [F,X] = ecdf(Y);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % INPUT
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 % - Y, a data series
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12 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % L Ferraioli 09-03-2011
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % $Id: ecdf.m,v 1.2 2011/03/09 11:40:27 luigi Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 function [F,X] = ecdf(Y)
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18
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % sort input data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 X = sort(Y);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % define variable for cumulative sum
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 sw = ones(size(X));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 n = numel(sw);
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25
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 jj = 2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 idd = false(size(sw));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % Fi is calculated practically as Fi = ni/n where ni is the position of
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 % the ith element of the sorted input array. If two or more elements are
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % equal then only the ni corresponding to the last one is considered and
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 % the other elements are removed. ni is obtained by a cumulative sum of
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 % an arrays of ones. If k elements are equal they are removed and
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 % substituted by a single k.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 while jj < n+1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 if X(jj) ~= X(jj-1); % if successive elements are different we can go on
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 jj = jj+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 else % if some elements are equal than we have to count the equal elements
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 jt = jj+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 while jt<=n+1 && X(jt-1)==X(jj-1) % counting equal elements
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 jt = jt + 1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 for ji=jj:jt-2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 idd(ji-1) = true; % make the assignement for successive removal of elements
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45 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 t = jt-jj;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 % set the value corresponding to the number of equal elements in
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 % correspondence to the last element of the series of eqials
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 sw(jt-2) = t;
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50
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 jj = jt;
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52 end
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53 end
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54
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 % remove unwanted elements corresponding to duplicates
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 sw(idd) = [];
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57
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 % calculate cumulative distribution by cumulative sum
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 F = cumsum(sw)./n;
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60
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 % remove elements corresponding to replicas
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 X(idd) = [];
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63
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64 end