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

Lévy
distribution

Common notation


Parameters

= scale
parameter ()

Domain


Probability density
function


Cumulative distribution
function


Mean


Variance


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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