Generating generalized inverse Gaussian random variates by fast inversion

Authors:
Josef Leydold;Wolfgang Hörmann
Affiliations:
Department of Statistics and Mathematics, WU (Vienna University of Economics and Business), Augasse 2-6, A-1090 Wien, Austria;Department of Industrial Engineering, Boğaziçi University, 34342 Bebek-İstanbul, Turkey
Venue:
Computational Statistics & Data Analysis
Year:
2011

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Abstract

The inversion method for generating non-uniformly distributed random variates is a crucial part in many applications of Monte Carlo techniques, e.g., when low discrepancy 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 to machine precision and they are much faster than root finding methods like the bisection method that has been recently proposed.