GB2Dist {brr} R Documentation

## Gamma-Beta2 distribution

### 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

```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

```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)
```

[Package brr version 1.0.0 Index]