The inverse Gaussian distribution
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While the Gaussian (i.e. normal distribution
describes a Brownian motion’s level at a fixed time, the inverse Gaussian
distribution describes the distribution of time a Brownian motion starting at 0
with positive drift takes to reach a fixed positive level.
![[SmartChart]](I/InverseGaussianDistribution_files/image001.gif)
![[SmartChart]](I/InverseGaussianDistribution_files/image002.gif)
![[SmartChart]](I/InverseGaussianDistribution_files/image003.gif)
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Distribution name
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Inverse Gaussian
distribution
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Common notation
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Parameters
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 =
parameter ( )
 =
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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(Excess) kurtosis
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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 “inverse
gaussian”. 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 “inverse gaussian3”, see also including
additional shift and scale parameters. For details of other supported
probability distributions see here.
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