I'm in electronic engineering rather than finance, but I found this useful because it crops up many times in engineering - thanks! However, I found that the derived Gumbel parameters aren't accurate for small values of n. I'm using Matlab BTW. The expected value is too low and the tail is too high. It seems that the PDF moves toward being normal as n is decreased. That seems reasonable because in the limit n=1 is back to the original normal distribution. But the Gumbel parameters from your quoted formula don't seem to get this right for small n. Any thoughts?