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If γ> 0, then the distribution is a Frechet-type GEV. Such distribution has a tail that follows a power law
If γ=0, then the distribution is a Gumbel-type GEV distribution. Here, the tail will be exponential, as with the normal and gamma distributions and their close relatives
If γ<0, then the distribution is a Weibull-type GEV distribution. This has a tail that falls off so quickly that there is actually a finite right endpoint to the distribution, as with the beta, uniform and triangular distributions. Given that EVT is used when there is concern about extreme observations, this suggests that Weibull-type GEV distribution is of little interest in this respect
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