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
θ + 2 π n − μ ≤ 0
Expressing the above pdf in terms of the characteristic function of the Lévy distribution yields: In terms of the circular variable
the circular moments of the wrapped Lévy distribution are the characteristic function of the Lévy distribution evaluated at integer arguments: where