This bootstrap test for the null hypothesis $H_0:$ a random sample has a gPd with unknown shape parameter $gamma$ is an intersection-union test for the hypotheses $H_0^-:$ a random sample has a gPd with $gamma <0 $,="" and="" $h_0^+:$="" a="" random="" sample="" has="" gpd="" with="" $gamma="">=0$.
Thus, heavy and non-heavy tailed gPd's are included in the null hypothesis. The parametric bootstrap is performed on $gamma$ for each of the two hypotheses.The gPd function with unknown shape and scale parameters $gamma$ and $sigma$ is given by
$$F(x) = 1 - \left[ 1 + \frac{\gamma x}{ \sigma } \right] ^ { - 1 /\gamma},$$
where $gamma$ is a real number, $sigma > 0$ and $1 + gamma x / sigma > 0$. When $gamma =
0$, F(x) becomes the exponential distribution with scale parameter $sigma$: $$F(x) = 1 -exp\left(-x/\sigma \right).$$