PGB2Dist {brr} R Documentation

## Poisson-Gamma-Beta2 distribution

### Description

Density and random generation for the Poisson-Gamma-Beta2 distribution with shape parameters `a`, `c`, `d` and hyperrate parameter `tau` (scale of the Beta2 distribution). For `tau=1` this is the same as the Beta-negative binomial distribution.

### Usage

```dPGB2(x, a, c, d, tau)

pPGB2(q, a, c, d, tau)

qPGB2(p, a, c, d, tau)

rPGB2(n, a, c, d, tau)

summary_PGB2(a, c, d, tau, output = "list")
```

### Arguments

 `x,q` vector of non-negative integer quantiles `a,c,d` non-negative shape parameters `tau` non-negative hyperrate parameter `p` vector of probabilities `n` number of observations to be sampled `output` type of the `summary_PGB2` 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, then sampling a value λ from the Gamma distribution with shape a and rate y, and then sampling the Poisson distribution with mean λ.

### Value

`dPGB2` gives the density, `pPGB2` the cumulative function, `rPGB2` samples from the distribution, and `summary_PGB2` gives a summary of the distribution.

### Note

`PGB2Dist` is a generic name for the functions documented.

### Examples

```a <- 2 ; c <- 5 ; d <- 30; tau <- 2
barplot(dPGB2(0:40, a, c, d, tau), names=0:40)
summary_PGB2(a,c,d,tau, output="pandoc")
```

[Package brr version 1.0.0 Index]