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Sample from the inverted gamma-2 distribution

Source: R/rig2.R
rig2.Rd

Samples independent random numbers from the inverted gamma-2 distribution, denoted by \(IG2(s, \nu)\), with density $$f(x) = \frac{(s/2)^{\nu/2}}{\Gamma(\nu/2)} x^{-(\nu+2)/2}\exp\left(-\frac{s}{2x}\right), \quad x > 0.$$ The draws are generated as \(s/Z\), where \(Z\) follows a chi-squared distribution with \(\nu\) degrees of freedom.

This distribution is commonly used for variance parameters in Bayesian models.

Usage

rig2(n, s, nu)

Arguments

n

a positive integer giving the number of draws. C++: an int object.

s

a positive real scalar giving the scale parameter. C++: a double object.

nu

a positive real scalar giving the degrees-of-freedom parameter. C++: a double object.

Value

A numeric vector of length n containing independent draws from the inverted gamma-2 distribution. C++: an arma::vec object.

Details

This function is based on C++ code from the GPL-3 R package bsvars by Woźniak (2024, 2025). It uses random-number generators from the armadillo library by Sanderson & Curtin (2025), made available to R through the RcppArmadillo package by Eddelbuettel et al. (2025).

References

Bauwens L., Lubrano M., Richard J.-F. (1999). Bayesian Inference in Dynamic Econometric Models. Oxford University Press.

Eddelbuettel D., François 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

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

Woźniak T. (2024). bsvars: Bayesian Estimation of Structural Vector Autoregressive Models, R package version 3.2. doi:10.32614/CRAN.package.bsvars

Woźniak T. (2025). Fast and Efficient Bayesian Analysis of Structural Vector Autoregressions Using the R Package bsvars. University of Melbourne Working Paper, 1–25. doi:10.48550/arXiv.2410.15090

Author

Tomasz Woźniak wozniak.tom@pm.me

Examples

rig2(5, 1, 10)
#>            [,1]
#> [1,] 0.06306287
#> [2,] 0.14042387
#> [3,] 0.06977329
#> [4,] 0.09247198
#> [5,] 0.12065217