Confidence Interval for an extreme value distribution

Hi!

I have a data set of output variables from a Monte Carlo simulation, which follow a Gumbel distribution. How do I determnie a 95 % confidence interval of my data based on the estimated distribution paramters? My data describes wind speeds. I want to say that a 95 % confidence interval covers a wind speed range from e.g. 10 to 20 m/s.

I've searched around in the statistical toolbox documentation, but can't find what I'm looking for.

Thank you! Tori

Answer 1

[Oleg Komarov]

http://www.mathworks.com/help/toolbox/stats/bqt29ct.html look for extreme value or generalized extreme value distributions.

• evinv
• gevinv

[Tori]

Thank you, but could you give me a more detailed description?

I have had a look at these functions, but cannot see how to use them to evaluate a Gumbel distribution.

[Oleg Komarov]

If you don't have the parameters of the distribution then use the corresponding fit functions:

[parmhat,parmci] = evfit(data)

where by default parmci are the values at the 95% confidence.

[Tori]

Thank you Oleg. I think I found the solution. I can use the evinv function to describe a Gumbel distribution if I "mirror" my distribution (multiply with -1). Do you agree with me that the line

X = evinv([0.025 0.975],muMLE,sigmaMLE)

where muMLE and sigmaMLE is the estimated distribution parameters, will give me a 95 % confidence interval in X?

[Oleg Komarov]

Yes, exactly.