Computes the cdf of AEP distribution given by
$$
F_{X}(x|\Theta)=
\frac{1-\epsilon}{2}-\frac{1-\epsilon}{2 \Gamma\bigl(1+\frac{1}{\alpha}\bigr)} \gamma\Bigl(\Big|\frac{\mu-x}{\sigma(1-\epsilon)}\Big|^{\alpha},\frac{1}{\alpha}\Bigr),~{}~x < \mu,
$$
$$
F_{X}(x|\Theta)=
\frac{1-\epsilon}{2}+\frac{1+\epsilon}{2 \Gamma\bigl(1+\frac{1}{\alpha}\bigr)} \gamma\Bigl(\Big|\frac{x-\mu}{\sigma(1+\epsilon)}\Big|^{\alpha},\frac{1}{\alpha}\Bigr),~{{}}~x \geq \mu,
$$
where \(-\infty<x<+\infty\), \(\Theta=(\alpha,\sigma,\mu,\epsilon)^T\) with \(0<\alpha \leq 2\), \(\sigma> 0\), \(-\infty<\mu<\infty\), and \(-1<\epsilon<1\).