R: The Generalised Beta Distribution

betagen {mc2d} | R Documentation

## The Generalised Beta Distribution

### Description

Density, distribution function, quantile function and random generation for the Beta distribution defined on the [min, max] domain with parameters shape1 and shape2 ( and optional non-centrality parameter ncp).

### Usage

    dbetagen(x, shape1, shape2, min=0, max=1, ncp=0, log=FALSE)
    pbetagen(q, shape1, shape2, min=0, max=1, ncp=0, lower.tail=TRUE,
    	  log.p=FALSE)
    qbetagen(p, shape1, shape2, min=0, max=1, ncp=0, lower.tail=TRUE,
    	  log.p=FALSE)
    rbetagen(n, shape1, shape2, min=0, max=1, ncp=0)

### Arguments

`x,q` | Vector of quantiles.
`p` | Vector of probabilities.
`n` | Number of observations. If length(n) > 1, the length is taken to be the number required.
`shape1, shape2` | Positive parameters of the Beta distribution.
`min` | Vector of minima.
`max` | Vector of maxima.
`ncp` | Non-centrality parameter of the Beta distribution.
`log, log.p` | Logical; if TRUE, probabilities p are given as log(p).
`lower.tail` | Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].

### Details

x ~ betagen(shape1, shape2, min, max, ncp)

if

(x-min)/(max-min)~beta(shape1,shape2,ncp)

These functions use the `Beta` distribution functions after correct parametrisation.

### Value

dbetagen gives the density, pbetagen gives the distribution function, qbetagen gives the quantile function, and rbetagen generates random deviates.

### See Also

`Beta`

### Examples

    curve(dbetagen(x, shape1=3, shape2=5, min=1, max=6), from = 0, to = 7)
    curve(dbetagen(x, shape1=1, shape2=1, min=2, max=5), from = 0, to = 7, lty=2, add=TRUE)
    curve(dbetagen(x, shape1=.5, shape2=.5, min=0, max=7), from = 0, to = 7, lty=3, add=TRUE)

[Package mc2d version 0.1-18 Index]