The Lévy distribution
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The time of hitting a single point (different
from the starting point of 0) of a Brownian motion without a mean drift follows
the Lévy distribution with .
With a mean drift it follows an inverse
Gaussian meaning that the Lévy distribution is a special case of the
inverse Gaussian distribution.
Distribution name
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Lévy
distribution
|
Common notation
|
|
Parameters
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= scale
parameter ()
|
Domain
|
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Probability density
function
|
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Cumulative distribution
function
|
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Mean
|
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Variance
|
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Skewness
|
undefined
|
(Excess) kurtosis
|
undefined
|
Characteristic function
|
|
Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “levy”.
Functions relating to a generalised version of this distribution including an
additional location (i.e. shift) parameter may be accessed by using a DistributionName
of “levy2”, see also including
additional shift and scale parameters. For details of other supported
probability distributions see here.
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