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

			(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)