# Beta2Dist: Beta distribution of the second kind In brr: Bayesian Inference on the Ratio of Two Poisson Rates

## Description

Density, distribution function, quantile function and random generation for the Beta distribution of the second kind with shape parameters `c` and `d` and scale parameter `scale`.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```dbeta2(x, c, d, scale, log = FALSE, ...) pbeta2(q, c, d, scale, ...) qbeta2(p, c, d, scale, ...) rbeta2(n, c, d, scale) summary_beta2(c, d, scale, output = "list", ...) ```

## Arguments

 `x,q` vector of quantiles `c,d` non-negative shape parameters `scale` non-negative scale parameter `log` logical; if true, returns the logarithm of the result `...` other arguments passed to `FDist` `p` vector of probabilities `n` number of observations to be simulated `output` type of the `summary_beta2` output: `"list"` to return a list, `"pandoc"` to print a table

## Details

The Beta distribution of the second kind with shape parameters c>0 and d>0 and scale parameter k>0 is the distribution of k*(U/(1-U)) where U is a random variable following the Beta distribution with shape parameters c and d.

## Value

`dbeta2` gives the density, `pbeta2` the distribution function, `qbeta2` the quantile function, and `rbeta2` generates random observations, and `summary_beta2` returns a summary of the distribution.

## Note

`Beta2Dist` is a generic name for the functions documented.

## Examples

 ```1 2 3 4``` ```curve(dbeta2(x, 3, 10, scale=2), from=0, to=3) u <- rbeta(1e5, 3, 10) lines(density(2*u/(1-u)), col="blue", lty="dashed") summary_beta2(3,10,2) ```

### Example output

```sh: 1: cannot create /dev/null: Permission denied
\$mode
[1] 0.3636364

\$mean
[1] 0.6666667

\$sd
[1] 0.4714045

\$Q1
[1] 0.3415147

\$Q2
[1] 0.5532558

\$Q3
[1] 0.8619625
```

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