NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET The Multiple Roots Simulation Algorithm, the Inverse Gaussian Distribution, and the Sufficient Conditional Monte Carlo Method

Michael, Schucany & Haas (1976) presented a method for the simulation of random variates using transformations with multiple roots. A generalization of this method to include vectorvalued transformations is given here. A short introduction to the inverse Gaussian distribution is given. The joint distribution of the sufficient statistic is well known, but the proof given here based on the Basu theorem is possibly new. The multiple roots simulation algorithm is related to the method for doing Monte Carlo simulations conditioned on a sufficient statistic presented by Lindqvist & Taraldsen (2005). The method is explained here by application on the inverse Gaussian distribution. The result is in this case an academic alternative to the much simpler and preferable method discovered by Cheng (1984) for doing Monte Carlo simulations from the inverse Gaussian distribution conditioned on the sufficient statistic. This means that the inverse Gaussian can be used as a non-trivial test case for a general numerical implementation of the sufficient conditional Monte Carlo method.