In probability theory and directional statistics, a wrapped Lévy distribution is a wrapped probability distribution that results from the "wrapping" of the Lévy distribution around the unit circle.

The pdf of the wrapped Lévy distribution is

where the value of the summand is taken to be zero when ${\displaystyle \theta +2\pi n-\mu \leq 0}$, ${\displaystyle c}$ is the scale factor and ${\displaystyle \mu }$ is the location parameter. Expressing the above pdf in terms of the characteristic function of the Lévy distribution yields:

In terms of the circular variable ${\displaystyle z=e^{i\theta }}$ the circular moments of the wrapped Lévy distribution are the characteristic function of the Lévy distribution evaluated at integer arguments:

where ${\displaystyle \Gamma \,}$ is some interval of length ${\displaystyle 2\pi }$. The first moment is then the expectation value of z, also known as the mean resultant, or mean resultant vector:

The mean angle is

and the length of the mean resultant is