Suppose two distributions F and G that have the same extreme point ($x^F = x^G$) and
$$\lim_{x \to x^F}\frac{\bar{F}(x)}{\bar{G}(x)} = c \in (0, \infty)$$
Show that F and G belongs to the same domain of attraction of a GEV$(0,1,\xi)$(Generalized extreme value). Also, provide a link between the normalization constants.
The definition I learned is that if F belongs to the domain of attraction of GEV(0,1,$\xi$) we will have $$h(x) = \frac{1-F(x)}{f(x)} \quad h'(x) \rightarrow \xi \text{ as } x \rightarrow x^F$$
I am pretty lost on how to prove it and any help would be appreciated.
