Let \mathcal{IG} denote the inverse Gaussian distribution and \mathcal{N} denote the normal distribution. Let z\sim\mathcal{IG}(\delta,\gamma), where \gamma=\sqrt{\alpha^2-\beta^2}; and let x\sim\mathcal{N}(\mu+\beta z,z), then x follows the NIG distribution, with parameters, \alpha,\beta,\delta,\mu. This can be used to generate NIG variates by ancestral sampling. It can also be used to derive an EM algorithm for maximum-likelihood estimation of the NIG parameters.
