The calculation process of the Lévy distribution is:
$$\mathrm{L\acute{e}vy}(\beta) \sim \frac{\varphi \times u}{|v|^\frac{1}{\beta}}$$
where $\mathrm{L\acute{e}vy}(\beta)$ is a Lévy random number obeying the Lévy distribution; $u$ and $v$ obey the standard normal distribution; $\beta$ is a constant value $0<\beta<2$.
The calculation formula of $\varphi$ is as follows:
$$\varphi = \left( \frac{\Gamma(1+\beta) \times \sin \big(\pi \times \frac{\beta}{2} \big)}{\Gamma \left( \big(\frac{1+\beta}{2} \big) \times \beta \times 2^{\frac{\beta-1}{2}} \right)} \right)^\frac{1}{\beta}$$
where $\Gamma()$ is the Gamma function.
I want to calculate:
$$R = \text{abs} \big(R_0 \times \mathrm{L\acute{e}vy}(\beta) \big)$$
but I don't know how to calculate $\mathrm{L\acute{e}vy}(\beta)$ or how to take the value of $u$ and $v$. How should this $\mathrm{L\acute{e}vy}(\beta)$ be calculated?
