Generating generalized inverse Gaussian random variates. (English) Zbl 1325.62031

Summary: The generalized inverse Gaussian distribution has become quite popular in financial engineering. The most popular random variate generator is due to J. S. Dagpunar [“An easily implemented generalised inverse Gaussian generator”, Commun. Stat., Simul. Comput. 18, 703–710 (1989)]. It is an acceptance-rejection algorithm method based on the Ratioof-Uniforms method. However, it is not uniformly fast as it has a prohibitive large rejection constant when the distribution is close to the gamma distribution. Recently some papers have discussed universal methods that are suitable for this distribution. However, these methods require an expensive setup and are therefore not suitable for the varying parameter case which occurs in, e.g., Gibbs sampling. In this paper we analyze the performance of Dagpunar’s algorithm and combine it with a new rejection method which ensures a uniformly fast generator. As its setup is rather short it is in particular suitable for the varying parameter case.


62E10 Characterization and structure theory of statistical distributions
65C10 Random number generation in numerical analysis
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