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)