- Description
- See also
- References
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
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
- Wrapped distribution
- Directional statistics
References
- {{cite book |title=Statistical Analysis of Circular Data |last=Fisher |first=N. I. |year=1996 |publisher=Cambridge University Press |location= |isbn=978-0-521-56890-6 |url=https://books.google.com/books?id=IIpeevaNH88C&dq=%22circular+variance%22+fisher&source=gbs_navlinks_s |accessdate=2010-02-09}}
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