Computes the quantile function of AEP distribution given by
$$
F_{X}^{-1}(u|\Theta)=
\mu-\sigma(1-\epsilon)\biggl[\frac{\gamma\bigl(\frac{1-\epsilon-2u}{1-\epsilon},\frac{1}{\alpha}\bigr)}{\Gamma\bigl(\frac{1}{\alpha}\bigr)}\biggr]^{\frac{1}{\alpha}},~{{}}~u\leq \frac{1-\epsilon}{2},
$$
$$
F_{X}^{-1}(u|\Theta)=
\mu+\sigma(1+\epsilon)\biggl[\frac{\gamma\bigl(\frac{2u+\epsilon-1}{1+\epsilon},\frac{1}{\alpha}\bigr)}{\Gamma\bigl(\frac{1}{\alpha}\bigr)}\biggr]^{\frac{1}{\alpha}},~{{}}~u> \frac{1-\epsilon}{2}.\\
$$
where
\(-\infty<x<+\infty\), \(\Theta=(\alpha,\sigma,\mu,\epsilon)^T\) with \(0<\alpha \leq 2, \sigma> 0\), \(-\infty<\mu<\infty\), \(-1<\epsilon<1\),
and
$$\gamma(u,\nu) =\int_{0}^{u}t^{\nu-1}\exp\bigl\{-t\bigr\}dt, ~\nu>0.$$