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Properties of the generalized inverse Gaussian with applications to Monte Carlo simulation and distribution function evaluation

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  • Peña, Víctor
  • Jauch, Michael

Abstract

We introduce two mixture representations for the generalized inverse Gaussian (GIG) distribution. One mixture representation expresses the GIG as a continuous mixture of inverse Gaussians. The other reveals a relationship between GIGs. These mixture representations lead to new sampling methods and an exact algorithm for evaluating the distribution function of the GIG for half-integer p.

Suggested Citation

  • Peña, Víctor & Jauch, Michael, 2025. "Properties of the generalized inverse Gaussian with applications to Monte Carlo simulation and distribution function evaluation," Statistics & Probability Letters, Elsevier, vol. 220(C).
    • Handle: RePEc:eee:stapro:v:220:y:2025:i:c:s0167715225000057
    DOI: 10.1016/j.spl.2025.110359
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    References listed on IDEAS

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    1. Kshitij Khare & Bala Rajaratnam & Abhishek Saha, 2018. "Bayesian inference for Gaussian graphical models beyond decomposable graphs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 727-747, September.
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    3. Willmot, Gordon E. & Woo, Jae-Kyung, 2022. "Remarks on a generalized inverse Gaussian type integral with applications," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    4. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    5. Alicia A. Johnson & Owen Burbank, 2015. "Geometric Ergodicity and Scanning Strategies for Two-Component Gibbs Samplers," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(15), pages 3125-3145, August.
    6. S. Favaro & A. Lijoi & I. Prünster, 2012. "On the stick-breaking representation of normalized inverse Gaussian priors," Biometrika, Biometrika Trust, vol. 99(3), pages 663-674.
    7. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
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