If $\xi < 0$, the GEV becomes the Weibull distribution, corresponding to the case where $F(x)$ has lighter than normal tails. This is precisely why the Weibull distribution is not used to model most empirical financial returns since only a few of them have light tails.

Things to Remember

1. The Generalized Extreme Value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory. It combines the Gumbel, Fréchet and Weibull families, also known as type I, II and III extreme value distributions. By varying the parameter $\xi$, the GEV distribution can model these three types of distributions.

2. When $\xi < 0$, the GEV becomes the Weibull distribution. The Weibull distribution has a cumulative distribution function with lighter than normal tails, meaning that extreme outcomes are less likely than under a normal distribution.

3. Financial returns are often heavy-tailed, meaning that extreme outcomes are more likely than under a normal distribution. This is due to the potential for significant market movements resulting from economic events, policy changes, or other factors.

4. Because of its lighter than normal tails, the Weibull distribution does not accurately reflect the distribution of most empirical financial returns, leading to its infrequent use in financial modeling.