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Generating generalized inverse Gaussian random variates by fast inversion

Author

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  • Leydold, Josef
  • Hörmann, Wolfgang

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.

Suggested Citation

  • Leydold, Josef & Hörmann, Wolfgang, 2011. "Generating generalized inverse Gaussian random variates by fast inversion," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 213-217, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:213-217
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    References listed on IDEAS

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    1. Lai, Yongzeng, 2009. "Generating inverse Gaussian random variates by approximation," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3553-3559, August.
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    Cited by:

    1. Xiaowen Dai & Libin Jin & Lei Shi, 2023. "Quantile regression in random effects meta-analysis model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 469-492, June.

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