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Samples random draws from the generalized inverse Gaussian distribution

Source: R/rgig1.R
rgig1.Rd

Samples random numbers from the generalized inverse Gaussian distribution with density proportional to: $$f(x) = x^{\lambda - 1} e^{-\frac{1}{2}(\chi/x + \psi x)},$$ with the parameters having to satisfy the conditions: $$% \begin{array}{l} \lambda > 0,\, \psi > 0, \chi \geq 0, \quad\mbox{or} \\ \lambda = 0,\, \psi > 0, \chi > 0, \quad\mbox{or} \\ \lambda < 0,\, \psi \geq 0, \chi > 0. \end{array} $$ The sampling algorithm proposed by Hörmann & Leydold (2013) is implemented. If the arguments do not satisfy the restrictions a std::logic_error exception is thrown in C++.

This method is useful for sampling variance coefficients that arise in problems with their likelihood in the form of th inverse gamma distribution and assuming a gamma prior.

Usage

rgig1(lambda, chi, psi)

Arguments

lambda

a real scalar representing parameter \(\lambda\). C++: a double object.

chi

a real scalar representing parameter \(\chi\). C++: a double object.

psi

a real scalar representing parameter \(\psi\). C++: a double object.

Value

random draw from the GIG distribution. C++: a double object.

Details

This function is based on C++ code from the R package shrinkTVP by Knaus, Bitto-Nemling, Cadonna, Frühwirth-Schnatter (2021) and also uses functionality of the GIGrvg package by Leydold & Hörmann (2023). It uses random number generators from the armadillo library by Sanderson & Curtin (2025) thanks to the RcppArmadillo package by Eddelbuettel, Francois, Bates, Ni, & Sanderson (2025)

References

Eddelbuettel D., Francois R., Bates D., Ni B., Sanderson C. (2025). RcppArmadillo: 'Rcpp' Integration for the 'Armadillo' Templated Linear Algebra Library. R package version 15.0.2-2. <doi:10.32614/CRAN.package.RcppArmadillo>

Hörmann W., Leydold J. (2013). Generating generalized inverse Gaussian random variates, Statistics and Computing 24, 547–557, <doi:10.1007/s11222-013-9387-3>.

Leydold J., Hörmann W. (2023). GIGrvg: Random Variate Generator for the GIG Distribution, R package version 0.8, <doi:10.32614/CRAN.package.GIGrvg>.

Knaus, P., Bitto-Nemling, A., Cadonna, A., & Frühwirth-Schnatter, S. (2021). Shrinkage in the Time-Varying Parameter Model Framework Using the R Package shrinkTVP. Journal of Statistical Software, 100(13), 1–32. <doi:10.18637/jss.v100.i13>.

Sanderson C., Curtin R. (2025). Armadillo: An Efficient Framework for Numerical Linear Algebra. International Conference on Computer and Automation Engineering, 303-307, <doi:10.1109/ICCAE64891.2025.10980539>

Author

Tomasz Woźniak wozniak.tom@pm.me

Examples

rgig1(1, 1, 1)
#> [1] 0.2440235