# GB2Dist: Gamma-Beta2 distribution In brr: Bayesian Inference on the Ratio of Two Poisson Rates

## Description

Density and random generation for the Gamma-Beta2 distribution with shape parameters `a`, `c`, `d` and rate parameter `tau` (scale of the Beta2 distribution).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```dGB2(x, a, c, d, tau) pGB2(q, a, c, d, tau, ...) qGB2(p, a, c, d, tau) rGB2(n, a, c, d, tau) moment_GB2(k, a, c, d, tau) summary_GB2(a, c, d, tau, output = "list", ...) ```

## Arguments

 `x,q` vector of non-negative quantiles `a,c,d` non-negative shape parameters `tau` non-negative rate parameter `...` arguemnts passed to `genhypergeo` function `p` vector of probabilities `n` number of observations to be sampled `k` the order of the moment `output` type of the `summary_GB2` output: `"list"` to return a list, `"pandoc"` to print a table

## Details

This is the mixture distribution obtained by sampling a value y from the Beta2 distribution with shape parameters c, d, and scale τ and then sampling a value from the Gamma distribution with shape a and rate y. The pdf involves the Kummer confluent hypergeometric function of the second kind. The cdf involves the generalized hypergeometric function. Its current implementation does not work when `a-d` is an integer, and also fails for many other cases.

## Value

`dGB2` gives the density, `pGB2` the cumulative function, `rGB2` samples from the distribution, and `summary_GB2` gives a summary of the distribution.

## Note

`GB2Dist` is a generic name for the functions documented.

## Examples

 ```1 2 3 4 5``` ```a <- 2 ; c <- 4 ; d <- 3; tau <- 1.67 sims <- rGB2(1e6, a, c, d, tau) mean(sims); moment_GB2(1,a,c,d,tau) mean(sims^2); moment_GB2(2,a,c,d,tau) summary_GB2(a,c,d,tau) ```

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