I'm currently reading up on extreme value theory and got stuck with the following problems/questions:
- Let's consider which consists of n independent normally distributed variables with zero mean and variance . As far as I understand, then the probability distribution of its maximum shows a Gumbel distribution with . Is there any way to determine and analytically?
- What is the effect of non-independency of the (in other words correlated variables)? Is there any well defined extreme value distribution resulting?
Thank you very much for you help (even references to corresponding papers/books)!
Best
Marc