📂Probability Distribution

Levy Distribution

Definition ¹

For scale $\gamma > 0$ and location $\delta \in \mathbb{R}$, the continuous probability distribution $\operatorname{Lévy} (\gamma, \delta)$ with the following probability density function is called the Lévy distribution. $$ f(x) = \sqrt{{\frac{ \gamma }{ 2 \pi }}} {\frac{ 1 }{ \left( x - \delta \right)^{3/2} }} \exp \left( - {\frac{ \gamma }{ 2 ( x - \delta ) }} \right) \qquad , x > \delta $$

Description

The Lévy distribution is one of the stable distributions and is less well known than other stable distributions such as the normal distribution or the Cauchy distribution. Note that it is not itself related to Lévy flights.