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matlabstatisticsdistribution
ian
ian

Reputation: 23

Matlab Gumbel Distribution (Extreme Maximum case)

The default MATLAB 'Extreme Value' distribution (also called a Gumbel distribution) is used for the extreme MIN case.

Given the mean and standard deviation of Gumbel distributed random variables for the extreme MAX case, I can get the location and scale parameter using the following equations from this website:

equations

My question is how do I transform the MATLAB 'Extreme Value' distribution from the MIN case to MAX case (MATLAB says "using the negative of the original values").

I would like to use MATLAB's icdf function, thus do I need to negate the location and scale parameters of the inputs?

Upvotes: 1

Views: 1724

Answers (2)

Amir
Amir

Reputation: 1

I have been working on the same problem and this is what I've concluded:

To create the probability distribution function of extreme value type I or gumbel for the maximum case in matlab using mu and sigma, or location and scale parameter, you can use the makedist function, use generalized extreme value function and set the k parameter equal to zero. This will create a mirror image of the ev, or extreme value function minimum which is used for gumbel in matlab. The mirror of the minimum case of gumbel is the maximum case of gumbel.

pd = makedist('GeneralizedExtremeValue','k',0,'sigma',sigma,'mu',mu);

so using the above command all you have to do is replace sigma and mu with the values you've got.

I am a student and this is my understanding of this problem.

Upvotes: 0

Chris
Chris

Reputation: 470

Judging by the last paragraph of your question you want the inverse CDF of the maximum Gumbel distribution. Given that Matlab offers the inverse CDF of the Gumbel min distribution as follows:

X = evinv(P,mu,sigma);

You can get the inverse CDF of the Gumbel max by:

X = -evinv(1-P, -mu, sigma);

Note that for computing the PDF or CDF different expressions hold (that can be similarly worked out based on the definition of the two distributions).

Upvotes: 1

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