# PGIBDist: Poisson-Gamma-Inverse Beta distribution In brr: Bayesian Inference on the Ratio of Two Poisson Rates

## Description

Density and random generation for the Poisson-Gamma-Inverse Beta distribution with shape parameters `a`, `c`, `d` and scale parameter `rho`.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```dPGIB(x, a, alpha, beta, rho) pPGIB(q, a, alpha, beta, rho) qPGIB(p, a, alpha, beta, rho) rPGIB(n, a, alpha, beta, rho) summary_PGIB(a, alpha, beta, rho, output = "list", ...) ```

## Arguments

 `x,q` vector of integer quantiles `a` non-negative shape parameter of the Gamma distribution `alpha,beta` non-negative shape parameters of the mixing Beta distribution `rho` hyperrate parameter (rate of the mixing distribution) `p` vector of probabilities `n` number of observations to be simulated `output` type of the `summary_PGIB` output: `"list"` to return a list, `"pandoc"` to print a table `...` arguments passed to `pander.data.frame`

## Details

This is the mixture distribution obtained by sampling a value from a Gamma-Inverse Beta distribution and then sampling from a Poisson distribution having this value as mean.

## Value

`dPGIB` gives the density, `rPGIB` samples from the distribution, and `summary_PGIB` gives a summary of the distribution.

## Note

`PGIBDist` is a generic name for the functions documented.

## Examples

 ```1 2``` ```barplot(dPGIB(0:5, a=13, alpha=4, beta=2, rho=2.5), names=0:5) summary_PGIB(13, 4, 2, 2.5) ```

brr documentation built on May 29, 2017, 3:10 p.m.