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.
![[SmartChart]](I/LevyDistribution_files/image003.gif)
![[SmartChart]](I/LevyDistribution_files/image004.gif)
![[SmartChart]](I/LevyDistribution_files/image005.gif)
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Distribution name
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Lévy
distribution
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Common notation
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Parameters
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 = scale
parameter ( )
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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
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undefined
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(Excess) kurtosis
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undefined
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Characteristic function
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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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