Wrapped Lévy distribution
The pdf of the wrapped Lévy distribution is
where the value of the summand is taken to be zero when , is the scale factor and 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 the circular moments of the wrapped Lévy distribution are the characteristic function of the Lévy distribution evaluated at integer arguments:
where is some interval of length . 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
- Fisher, N. I. (1996). Statistical Analysis of Circular Data. Cambridge University Press. ISBN 978-0-521-56890-6. Retrieved 2010-02-09.