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.
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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
References
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Discrete univariate with finite support | |
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Discrete univariate with infinite support | |
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Continuous univariate supported on a bounded interval | |
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Continuous univariate supported on a semi-infinite interval | |
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Continuous univariate supported on the whole real line | |
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Continuous univariate with support whose type varies | |
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Mixed continuous-discrete univariate | |
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Multivariate (joint) | |
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Directional | |
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Degenerate and singular | |
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Families | |
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This page was last edited on 13 December 2020, at 04:51