# Extreme Value Theory - Normalizing constants for Generalized Extreme Value distribution

I'm working on Extreme Values Theory, and I found the following sufficient condition to find the domain of attraction of a distribution and the corresponding normalizing constants:

For sufficiently smooth distribution $F$ with density $f$, define $\displaystyle h(x) = \frac{1-F(x)}{f(x)}$; let $\displaystyle b_n = F^{-1} \left( 1 - \frac{1}{n} \right)$, $a_n = h(b_n)$ and $\displaystyle \xi = \lim_{x \rightarrow +\infty}{h'(x)}$. Then the distribution of the maxima $F^n(a_nx+b_n)$ converges to a GEV distribution with shape parameter $\xi$.

My questions:

1. What are the exact conditions for this result? I guess "sufficiently smooth" means that there must exist a density; there is also a definition problem for $h(x)$ if $f(x)=0$: what are exactly the assumptions here?

2. I've got a theoretical book on Extreme Values (Resnick 87) but I haven't found this result; so how do you prove it?

Thanks

Note that the right endpoint $x^*$ of a distribution function $F$ is defined as $x^*=\sup\{x: F(x)<1\}$.