Using Gumbel distribution to calculate extreme events.

(Assuming that the true extreme event behavior follows a Gumbel distribution, determine the highest wind speeds expected with 1, 10, and 100 year return periods)

Here is what I have so far written for the code. I viewed help pages on matlab for computing extreme events using gumbel, but still cannot figure this out. If anyone could offer any help or advice it would be greatly appreciated. Thanks!

%Given info

%years, y

y = 2003:2012;

%maximum 10-minute average wind speed, ws2

ws2 = [ 18.2 19.7 21.2 17.9 23.5 20.1 19.6 20.4 20.3 24.8];

w2 = mean(ws2);

%Reference height, h2

h2 = 5;

%Hub height, H2

H2 = 80;

%Power law exponent, pc2

pc2 = 0.14;

%Equations

%Power law is u(z) = (U(Zr))*((z/Zr)^power law exponent)

u2 = (w2)*((H2/h2)^pc2);

%Gumbel distribution

Answer 1

[Tom Lane]

If you have the Statistics Toolbox, take a look at "help evfit" and pay particular attention to the statement at the bottom about Gumbel. I don't understand enough about what you are doing. It may be that you need to do something like

p = fitdist(-ws2','ev')

and then compute something like

yr = [1 10 100];
icdf(p, .5 ./ yr)

But you or your instructor would know better than I how you define the values for different return periods.

If you need the reference and hub heights and the exponent, even though they weren't mentioned in the original problem statement, I can't help with that.