The inversionmethod for generating non-uniformly distributed randomvariates is a crucial part inmany applications ofMonte Carlo techniques, e.g., when lowdiscrepancy sequences or copula based models are used. Unfortunately, closed form expressions of quantile functions of important distributions are often not available. The (generalized) inverse Gaussian distribution is a prominent example. It is shown that algorithms that are based on polynomial approximation are well suited for this distribution. Their precision is close tomachine precision and they aremuch faster than root findingmethods like the bisection method that has been recently proposed. © 2010 Elsevier B.V. All rights reserved.