Wrapped Lévy distribution

From Wikipedia, the free encyclopedia
  (Redirected from Wrapped Levy distribution)
Jump to: navigation, search

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.

Description[edit]

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

See also[edit]

References[edit]