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The goal of pg is to provide both R and C++ header access to the Polya Gamma distribution sampling routine.


You can install the development version of pg from GitHub with:

# install.packages("devtools")


Let X be a Polya Gamma Distribution denoted by PG(h, z), where h is the “shape” parameter and z is the “scale” parameter. Presently, the following sampling cases are enabled:

Not implemented:

The package structure allows for the sampling routines to be accessed either via C++ or through R. The return type can be either a single value or a vector. When repeat sampling is needed with the same b and c, please use the vectorized sampler.

Sampling with C++

Using the sampling routine in C++ through a standalone .cpp file requires either the rpg_scalar_hybrid(), rpg_vector_hybrid(), or rpg_hybrid() function to be accessed in the pg C++ namespace. Each of these functions will automatically select the appropriate algorithm based on criteria discussed previously.

#include <pg.h>
// [[Rcpp::depends(RcppArmadillo, pg)]]

// [[Rcpp::export]]
double rpg_scalar(const double h, const double z) {
  return pg::rpg_scalar_hybrid(h, z);

// [[Rcpp::export]]
arma::vec rpg_hybrid(const arma::vec& h, const arma::vec& z) {
  return pg::rpg_hybrid(h, z);

// [[Rcpp::export]]
arma::vec rpg_vector(unsigned int n, const double h, const double z) {
  return pg::rpg_vector_hybrid(n, h, z);

For use within an R package, include a the pg package name in the DESCRIPTION file. From there, include the pg.h header in a similar manner to the stand-alone C++ example.


Sampling with R

For use within an R file, you can do:

# Number of observations to sample
n = 4
# Select the PG(h, z) values
h = 1; z = 0.5

# Set a seed for reproducibility

# Sample a single observation
pg::rpg_scalar(h, z)
#> [1] 0.05752942

# Set a seed for reproducibility

# Sample a vector of observations
pg::rpg_vector(n, h, z)
#>            [,1]
#> [1,] 0.05752942
#> [2,] 0.38752679
#> [3,] 0.38710433
#> [4,] 0.18847913

See also

The following are useful resources regarding the Polya Gamma distribution.


James Balamuta leaning heavily on work done in BayesLogit R package by Nicholas G. Polson, James G. Scott, and Jesse Windle.

Citing the pg package

To ensure future development of the package, please cite pg package if used during an analysis or simulation study. Citation information for the package may be acquired by using in R:



GPL (>= 3)