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annotate m-toolbox/classes/+utils/@math/cdfplot.m @ 49:0bcdf74587d1 database-connection-manager

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Cleanup
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 07 Dec 2011 17:24:36 +0100
parents f0afece42f48
children
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % CDFPLOT makes cumulative distribution plot
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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 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 % h = cdfplot(y1,[],ops) Plot an empirical cumulative distribution function
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % against a theoretical cdf.
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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 % h = cdfplot(y1,y2,ops) Plot two empirical cumulative distribution
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % functions. Cdf for y1 is compared against cdf for y2 with confidence
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % bounds.
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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 % ops is a cell aray of options
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % - 'ProbDist' -> theoretical distribution. Available distributions are:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % - 'Fdist' -> F cumulative distribution function. In this case the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % parameter 'params' should be a vector with distribution degrees of
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % freedoms [dof1 dof2]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % - 'Normdist' -> Normal cumulative distribution function. In this case
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % the parameter 'params' should be a vector with distribution mean and
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % standard deviation [mu sigma]
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % - 'Chi2dist' -> Chi square cumulative distribution function. In this
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % case the parameter 'params' should be a number indicating
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % distribution degrees of freedom
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % - 'GammaDist' -> Gamma distribution. 'params' should contain the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % shape and scale parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % - 'ShapeParam' -> In the case of comparison of a data series with a
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 % theoretical distribution and the data series is composed of correlated
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % elements. K can be adjusted with a shape parameter in order to recover
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 % test fairness. In such a case the test is performed for K* = Phi *K.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % Phi is the corresponding Shape parameter. The shape parameter depends
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 % on the correlations and on the significance value. It does not depend
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % on data length.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 % - 'params' -> Probability distribution parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 % - 'conflevel' -> requiered confidence for confidence bounds evaluation.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33 % Default 0.95 (95%)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 % - 'FontSize' -> Font size for axis. Default 22
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 % - 'LineWidth' -> line width. Default 2
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 % - 'axis' -> set axis properties of the plot. refer to help axis for
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 % further details
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 % Luigi Ferraioli 10-02-2011
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 % % $Id: cdfplot.m,v 1.8 2011/07/08 09:45:48 luigi Exp $
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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 function h = cdfplot(y1,y2,ops)
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44
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 %%% check and set imput options
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 % Default input struct
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 defaultparams = struct(...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 'ProbDist','Fdist',...
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49 'ShapeParam',1,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 'params',[1 1],...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 'conflevel',0.95,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 'FontSize',22,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 'LineWidth',2,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 'axis',[]);
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55
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 names = {'ProbDist','ShapeParam','params','conflevel','FontSize','LineWidth','axis'};
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57
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 % collecting input and default params
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 if nargin == 3
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 if ~isempty(ops)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 for jj=1:length(names)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 if isfield(ops, names(jj))
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 defaultparams.(names{1,jj}) = ops.(names{1,jj});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 end
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65 end
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66 end
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67 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 pdist = defaultparams.ProbDist; % check theoretical distribution
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 shp = defaultparams.ShapeParam;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 dof = defaultparams.params; % distribution parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 conf = defaultparams.conflevel; % confidence level for confidence bounds calculation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 if conf>1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 conf = conf/100;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 fontsize = defaultparams.FontSize;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 lwidth = defaultparams.LineWidth;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 axvect = defaultparams.axis;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 %%% check data input
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 if isempty(y2) % do theoretical comparison
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 % get empirical distribution for input data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 [eCD,ex]=utils.math.ecdf(y1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 % switch between input theoretical distributions
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 switch lower(pdist)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87 case 'fdist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 CD = utils.math.Fcdf(ex,dof(1),dof(2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 case 'normdist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90 CD = utils.math.Normcdf(ex,dof(1),dof(2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 case 'chi2dist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 CD = utils.math.Chi2cdf(ex,dof(1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 case 'gammadist'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94 CD = gammainc(ex./dof(2),dof(1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 % get confidence levels with Kolmogorow - Smirnov test
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 alp = (1-conf)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 cVal = utils.math.SKcriticalvalues(numel(ex)*shp,[],alp);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 % get confidence levels
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 CDu = CD+cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 CDl = CD-cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 figure;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104 h = stairs(ex,[eCD CD CDu CDl]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105 grid on
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 xlabel('x','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107 ylabel('F(x)','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108 set(h(3:4), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109 set(h(1), 'Color','r', 'LineStyle','-','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110 set(h(2), 'Color','k', 'LineStyle','--','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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111 legend([h(1),h(2),h(3)],{'eCDF','CDF','Conf. Bounds'});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 if ~isempty(axvect)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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113 axis(axvect);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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114 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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115 % get limit for quantiles corresponding to 0 and 0.99 prob
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116 xlw = interp1(eCD,ex,0.001,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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117 if isnan(xlw)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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118 xlw = min(ex);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120 xup = interp1(eCD,ex,0.999,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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121 axis([xlw xup 0 1]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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122 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 else % do empirical comparison
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 % get empirical distribution for input data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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126 [eCD1,ex1]=utils.math.ecdf(y1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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127 [eCD2,ex2]=utils.math.ecdf(y2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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128
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Daniele Nicolodi <nicolodi@science.unitn.it>
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129 % get confidence levels with Kolmogorow - Smirnov test
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Daniele Nicolodi <nicolodi@science.unitn.it>
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130 alp = (1-conf)/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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131 cVal = utils.math.SKcriticalvalues(numel(ex1),numel(ex2),alp);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 % get confidence levels
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Daniele Nicolodi <nicolodi@science.unitn.it>
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133 CDu = eCD2+cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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134 CDl = eCD2-cVal;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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135
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Daniele Nicolodi <nicolodi@science.unitn.it>
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136 figure;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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137 h1 = stairs(ex1,eCD1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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138 grid on
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Daniele Nicolodi <nicolodi@science.unitn.it>
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139 hold on
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Daniele Nicolodi <nicolodi@science.unitn.it>
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140 h2 = stairs(ex2,[eCD2 CDu CDl]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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141 xlabel('x','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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142 ylabel('F(x)','FontSize',fontsize);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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143 set(h2(2:3), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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144 set(h1(1), 'Color','r', 'LineStyle','-','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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145 set(h2(1), 'Color','k', 'LineStyle','--','LineWidth',lwidth);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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146 legend([h1(1),h2(1),h2(2)],{'eCDF1','eCDF2','Conf. Bounds'});
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Daniele Nicolodi <nicolodi@science.unitn.it>
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147 if ~isempty(axvect)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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148 axis(axvect);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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149 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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150 % get limit for quantiles corresponding to 0 and 0.99 prob
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Daniele Nicolodi <nicolodi@science.unitn.it>
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151 xlw = interp1(eCD2,ex2,0.001,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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152 if isnan(xlw)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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153 xlw = min(ex2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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154 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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155 xup = interp1(eCD2,ex2,0.999,'linear');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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156 axis([xlw xup 0 1]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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157 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
158 h = [h1; h2];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
159 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
160
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
161 end