+
−% CDFPLOT makes cumulative distribution plot
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
−% 
+
−% h = cdfplot(y1,[],ops) Plot an empirical cumulative distribution function
+
−% against a theoretical cdf.
+
−% 
+
−% h = cdfplot(y1,y2,ops) Plot two empirical cumulative distribution
+
−% functions. Cdf for y1 is compared against cdf for y2 with confidence
+
−% bounds.
+
−% 
+
−% ops is a cell aray of options
+
−%   - 'ProbDist' -> theoretical distribution. Available distributions are:
+
−%     - 'Fdist' -> F cumulative distribution function. In this case the
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−%     parameter 'params' should be a vector with distribution degrees of
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−%     freedoms [dof1 dof2]
+
−%     - 'Normdist' -> Normal cumulative distribution function. In this case
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−%     the parameter 'params' should be a vector with distribution mean and
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−%     standard deviation [mu sigma]
+
−%     - 'Chi2dist' -> Chi square cumulative distribution function. In this
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−%     case the parameter 'params' should be a number indicating
+
−%     distribution degrees of freedom
+
−%     - 'GammaDist' -> Gamma distribution. 'params' should contain the
+
−%     shape and scale parameters
+
−%   - 'ShapeParam' -> In the case of comparison of a data series with a
+
−%   theoretical distribution and the data series is composed of correlated
+
−%   elements. K can be adjusted with a shape parameter in order to recover
+
−%   test fairness. In such a case the test is performed for K* = Phi *K.
+
−%   Phi is the corresponding Shape parameter. The shape parameter depends
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−%   on the correlations and on the significance value. It does not depend
+
−%   on data length. 
+
−%   - 'params' -> Probability distribution parameters
+
−%   - 'conflevel' -> requiered confidence for confidence bounds evaluation.
+
−%   Default 0.95 (95%)
+
−%   - 'FontSize' -> Font size for axis. Default 22
+
−%   - 'LineWidth' -> line width. Default 2
+
−%   - 'axis' -> set axis properties of the plot. refer to help axis for
+
−%   further details
+
−% 
+
−% Luigi Ferraioli 10-02-2011
+
−% 
+
−% % $Id: cdfplot.m,v 1.8 2011/07/08 09:45:48 luigi Exp $
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
−function h = cdfplot(y1,y2,ops)
+
−  
+
−  %%% check and set imput options
+
−  % Default input struct
+
−  defaultparams = struct(...
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−    'ProbDist','Fdist',...
+
−    'ShapeParam',1,...
+
−    'params',[1 1],...
+
−    'conflevel',0.95,...
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−    'FontSize',22,...
+
−    'LineWidth',2,...
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−    'axis',[]);
+
−  
+
−  names = {'ProbDist','ShapeParam','params','conflevel','FontSize','LineWidth','axis'};
+
−  
+
−  % collecting input and default params
+
−  if nargin == 3
+
−    if ~isempty(ops)
+
−      for jj=1:length(names)
+
−        if isfield(ops, names(jj))
+
−          defaultparams.(names{1,jj}) = ops.(names{1,jj});
+
−        end
+
−      end
+
−    end
+
−  end
+
−  
+
−  pdist = defaultparams.ProbDist; % check theoretical distribution
+
−  shp = defaultparams.ShapeParam;
+
−  dof = defaultparams.params; % distribution parameters
+
−  conf = defaultparams.conflevel; % confidence level for confidence bounds calculation
+
−  if conf>1
+
−    conf = conf/100;
+
−  end
+
−  fontsize = defaultparams.FontSize;
+
−  lwidth = defaultparams.LineWidth;
+
−  axvect = defaultparams.axis;
+
−
+
−  
+
−  %%% check data input
+
−  if isempty(y2) % do theoretical comparison
+
−    % get empirical distribution for input data
+
−    [eCD,ex]=utils.math.ecdf(y1);
+
−    % switch between input theoretical distributions
+
−    switch lower(pdist)
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−      case 'fdist'
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−        CD = utils.math.Fcdf(ex,dof(1),dof(2));
+
−      case 'normdist'
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−        CD = utils.math.Normcdf(ex,dof(1),dof(2));
+
−      case 'chi2dist'
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−        CD = utils.math.Chi2cdf(ex,dof(1));
+
−      case 'gammadist'
+
−        CD = gammainc(ex./dof(2),dof(1));
+
−    end
+
−    % get confidence levels with Kolmogorow - Smirnov test
+
−    alp = (1-conf)/2;
+
−    cVal = utils.math.SKcriticalvalues(numel(ex)*shp,[],alp);
+
−    % get confidence levels
+
−    CDu = CD+cVal;
+
−    CDl = CD-cVal;
+
−    
+
−    figure;
+
−    h = stairs(ex,[eCD CD CDu CDl]);
+
−    grid on
+
−    xlabel('x','FontSize',fontsize);
+
−    ylabel('F(x)','FontSize',fontsize);
+
−    set(h(3:4), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
+
−    set(h(1), 'Color','r', 'LineStyle','-','LineWidth',lwidth);
+
−    set(h(2), 'Color','k', 'LineStyle','--','LineWidth',lwidth);
+
−    legend([h(1),h(2),h(3)],{'eCDF','CDF','Conf. Bounds'});
+
−    if ~isempty(axvect)
+
−      axis(axvect);
+
−    else
+
−      % get limit for quantiles corresponding to 0 and 0.99 prob
+
−      xlw = interp1(eCD,ex,0.001,'linear');
+
−      if isnan(xlw)
+
−        xlw = min(ex);
+
−      end
+
−      xup = interp1(eCD,ex,0.999,'linear');
+
−      axis([xlw xup 0 1]);
+
−    end
+
−    
+
−  else % do empirical comparison
+
−    % get empirical distribution for input data
+
−    [eCD1,ex1]=utils.math.ecdf(y1);
+
−    [eCD2,ex2]=utils.math.ecdf(y2);
+
−    
+
−    % get confidence levels with Kolmogorow - Smirnov test
+
−    alp = (1-conf)/2;
+
−    cVal = utils.math.SKcriticalvalues(numel(ex1),numel(ex2),alp);
+
−    % get confidence levels
+
−    CDu = eCD2+cVal;
+
−    CDl = eCD2-cVal;
+
−    
+
−    figure;
+
−    h1 = stairs(ex1,eCD1);
+
−    grid on
+
−    hold on
+
−    h2 = stairs(ex2,[eCD2 CDu CDl]);
+
−    xlabel('x','FontSize',fontsize);
+
−    ylabel('F(x)','FontSize',fontsize);
+
−    set(h2(2:3), 'Color','b', 'LineStyle',':','LineWidth',lwidth);
+
−    set(h1(1), 'Color','r', 'LineStyle','-','LineWidth',lwidth);
+
−    set(h2(1), 'Color','k', 'LineStyle','--','LineWidth',lwidth);
+
−    legend([h1(1),h2(1),h2(2)],{'eCDF1','eCDF2','Conf. Bounds'});
+
−    if ~isempty(axvect)
+
−      axis(axvect);
+
−    else
+
−      % get limit for quantiles corresponding to 0 and 0.99 prob
+
−      xlw = interp1(eCD2,ex2,0.001,'linear');
+
−      if isnan(xlw)
+
−        xlw = min(ex2);
+
−      end
+
−      xup = interp1(eCD2,ex2,0.999,'linear');
+
−      axis([xlw xup 0 1]);
+
−    end
+
−    h = [h1; h2];
+
−  end
+
−  
+
−end