MATLAB: Problem in plotting confidence interval in a probability plot

statistics

i have performed extreme distribution to a data set.I intended to draw 95% confidence interval in the probability plot.The following codding was used:
WL= [ 6.79 6.89 6.38 5.67 6.91 7.66 6.41 6.04 6.41 5.55 6.93 5.67 6.69 6.51 6.32 7.33 6.43 6.52 6.13 6.72 6.7 7.78 6.18 5.41 6.94 6.51 6.02 5.94 6.08 ]; % observed water level data pd = fitdist(WL','ev'); % Creates a ProbDistUnivParam object by fitting the data to a extreme value distribution. ci = paramci(pd); % This function calculates the values of the parameters based on a certain confidence interval. Here the by default the confidence interval is 95 percent probplot(WL); h=probplot(gca,@(WL,x,y)evcdf(WL,x,y),[ci(1,1),ci(1,2)]); set(h,'color','r','linestyle','-') t= probplot(gca,@(WL,x,y)evcdf(WL,x,y),[ci(2,1),ci(2,2)]); set(t,'color','g','linestyle','-.')
But there is a problem in confidence interval line(green one) which deviated in a wrong way.there might be some error in ci(confidence interval) boundary but i could not fix it.please help me out.

Best Answer

I thing there are two problems with your approach. One is that you could simplify your code like this:
 WL= [ 6.79 6.89 6.38 5.67 6.91 7.66 6.41 6.04 6.41 5.55 6.93 5.67 6.69 6.51 6.32 7.33 6.43 6.52 6.13 6.72 6.7 7.78 6.18 5.41 6.94 6.51 6.02 5.94 6.08 ];
% observed water level data 

pd = fitdist(WL','ev');
% Creates a ProbDistUnivParam object by fitting the data to a extreme value distribution. 

ci = paramci(pd); 
% This function calculates the values of the parameters based on a certain confidence interval. Here the by default the confidence interval is 95 percent 

probplot('extreme value' , WL); 
h=probplot(gca,@evcdf,[ci(1,1),ci(1,2)]); 
set(h,'color','r','linestyle','-') 
t= probplot(gca,@evcdf,[ci(2,1),ci(2,2)]); 
set(t,'color','g','linestyle','-.')
Note that probplot is by default a normal distribution. You should specify whenever you use a different distribution. Secondly, what makes you think that there is an error with what you did? This is not curve fitting, you are comparing cdfs. There is no reason why the parameters you obtained from ci will give you two cdf's "above" and "below" the best fit cdf. You probably expect that from vanilla curve fitting. But these are not the "curves" you fitted to, these are cdf's.
Please take a look at the cdf's, as they might help you understand better:
 WL= [ 6.79 6.89 6.38 5.67 6.91 7.66 6.41 6.04 6.41 5.55 6.93 5.67 6.69 6.51 6.32 7.33 6.43 6.52 6.13 6.72 6.7 7.78 6.18 5.41 6.94 6.51 6.02 5.94 6.08 ];
% observed water level data 
pd = fitdist(WL','ev');
% Creates a ProbDistUnivParam object by fitting the data to a extreme value distribution. 
ci = paramci(pd); 
% This function calculates the values of the parameters based on a certain confidence interval. Here the by default the confidence interval is 95 percent 
evBest = @(x) evcdf(x,pd.Params(1),pd.Params(2));
evLow =  @(x) evcdf(x,ci(1,1),ci(1,2));
evHigh =  @(x) evcdf(x,ci(2,1),ci(2,2));
 fplot(evBest,[0 10],'k--');
 hold on
 fplot(evLow,[0 10],'r-');
 fplot(evHigh,[0 10],'b-');
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