The density function \(f_{P}(p|\alpha)\), of positive \(\alpha\)-stable distribution is given by (Kanter, 1975):
$$
f_{P}(p|\alpha)=\frac{1}{\pi}\int_{0}^{\pi}{\frac{\alpha}{2-\alpha}}a(\theta) p^{-\frac{\alpha}{2-\alpha}-1}a(\theta) \exp\Bigl\{-p^{-\frac{\alpha}{2-\alpha}}a(\theta)\Bigr\}d\theta, $$
where \(0<\alpha \leq 2\) is tail thickness parameter or index of stability and
$$
a(\theta)=\frac{\sin\Bigl(\bigl(1-\frac{\alpha}{2}\bigr)\theta\Bigr)\Bigl[\sin \bigl(\frac{\alpha \theta}{2}\bigr)\Bigr]^{\frac{\alpha}{2-\alpha}}}{[\sin(\theta)]^{\frac{2}{2-\alpha}},}
$$
for \(0<\theta < \pi\). We use the Monte Carlo method for approximating \(f_{P}(p|\alpha)\).