Inverse Gaussian Distribution
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المرجع الالكتروني للمعلوماتيه
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www.almerja.com
الجزء والصفحة:
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7-4-2021
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Inverse Gaussian Distribution
The inverse Gaussian distribution, also known as the Wald distribution, is the distribution over 
with probability density function and distribution function given by
where 
is the mean and 
is a scaling parameter.
The inverse Gaussian distribution is implemented in the Wolfram Language as InverseGaussianDistribution[mu, lambda].
The 
th raw moment is given by
 |
(3)
|
where 
is a modified Bessel function of the second kind, giving the first few as
Using 
gives a recursion relation for the raw moments as
 |
(7)
|
The first few central moments are
The cumulants 
are given by
 |
(11)
|
The variance, skewness, and kurtosis excess are given by
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