The inverse Gaussian distribution, also known as the Wald distribution, is the distribution over with probability density function and distribution function given by
(1)
| |||
(2)
|
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
(4)
| |||
(5)
| |||
(6)
|
Using gives a recursion relation for the raw moments as
(7)
|
The first few central moments are
(8)
| |||
(9)
| |||
(10)
|
The cumulants are given by
(11)
|
The variance, skewness, and kurtosis excess are given by
(12)
| |||
(13)
| |||
(14)
|