Generating inverse Gaussian random variates by approximation

The inverse Gaussian distribution is a useful distribution with important applications. But there is less discussion in the literature on sampling of this distribution. The method given in [Atkinson, A.C., 1982. The simulation of generalized inverse Gaussian and hyperbolic random variables. SIAM Journal on Scientific and Statistical Computing 3(4), 502–515] is based on rejection method where some (uniform) random numbers from the sample are discarded. This feature makes it difficult to take advantage of the low discrepancy sequences which have important applications. In [Michael, J., Schucany, W., Haas, R., 1976. Generating random variates using transformations with multiple roots. The American Statistician 30(2), 88–90], Michael et al. give a method to generate random variables with inverse Gaussian distribution. In their method, two pseudorandom numbers uniformly distributed on (0, 1) are needed in order to generate one inverse Gaussian random variable. In this short paper, we present a new method, based on direct approximate inversion, to generate the inverse Gaussian random variables. In this method, only one pseudorandom number is needed in generating one inverse Gaussian random variate. This method enables us to make use of the better convergence of low discrepancy sequence than the pseudorandom sequence. Numerical results show the superiority of low discrepancy sequence than the pseudorandom sequence in simulating the mean of the inverse Gaussian distribution by using our sampling method. Further application of this method in exotic option pricing under the normal inverse Gaussian model is under investigation.