Fit distribution to probability plot

Is it possible to fit a Generalized Extreme Value distribution to a probability plot? I've got 31 annual highest values that I have plotted in a probabilty plot using >>probplot(a); and now I want a distribution fitted to the data Points. How can I do this?

I've tried using gevfit to find the parameters for the distribution and i tried plotting gevpdf(a,0,107,399) in a probability plot but it didn't give me what I wanted, I just got this:

but I want something looking like this:

Thanks!

Answer 1

[Brendan Hamm]

It looks like you are looking at comparing the Cumulative Distribution Function (CDF) with the Empirical Cumulative Distribution Function (ECDF) which is not the same as a probability plot.

I'll start by generating some random numbers from an EVD as I do not have your data:

rng('default')
a = gevrnd(0,107,399,100,1);

Next we need to fit the parameters of the distribution:

Mdl = fitdist(a,'GeneralizedExtremeValue'); % Returns a PD object (Requires MATLAB later than 2009)

You can then calculate the ECDF: [f,x] = ecdf(a); % plot(x,f)

Then calculate the CDF implied by the fitted parameters:

y = cdf(Mdl,x);
hold on
plot(x,y)
hold off

If you indeed wanted to look at a probability plot, you should know that by default probplot compares the data with a normal distribution. To change this, pass in the name of the distribution:

figure
probplot('extreme value',a)

[Gustav Lindstrand]

Thank you so much!

Is there a way to make the fit "keep going"? Now the fit ends when my data ends, I would like it to keep going so that I can look up the value at the probability 0.99 (for example)

[Brendan Hamm]

The fit itself is defined on the entire support of the distribution. The PD objects are very useful for problems like what you mention. You can find a list of the methods (special functions) available for the PD objects.

methods(Mdl) % prints a list of the methods for the object.

To find the value at the 0.99 probability you would want the icdf method:

CDFval99 = icdf(Mdl,0.99)