betareg

The Extended-Support Beta Distribution

Description

Density, distribution function, quantile function, and random generation for the extended-support beta distribution (in regression parameterization) on [0, 1].

Usage

dxbeta(x, mu, phi, nu = 0, log = FALSE)

pxbeta(q, mu, phi, nu = 0, lower.tail = TRUE, log.p = FALSE)

qxbeta(p, mu, phi, nu = 0, lower.tail = TRUE, log.p = FALSE)

rxbeta(n, mu, phi, nu = 0)

Arguments

`x`, `q`	numeric. Vector of quantiles.
`p`	numeric. Vector of probabilities.
`n`	numeric. Number of observations. If `length(n) > 1`, the length is taken to be the number required.
`mu`	numeric. The mean of the underlying beta distribution on [-nu, 1 + nu].
`phi`	numeric. The precision parameter of the underlying beta distribution on [-nu, 1 + nu].
`nu`	numeric. Exceedence parameter for the support of the underlying beta distribution on [-nu, 1 + nu] that is censored to [0, 1].
`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

In order to obtain an extended-support beta distribution on [0, 1] an additional exceedence parameter nu is introduced. If nu > 0, this scales the underlying beta distribution to the interval [-nu, 1 + nu] where the tails are subsequently censored to the unit interval [0, 1] with point masses on the boundaries 0 and 1. Thus, nu controls how likely boundary observations are and for nu = 0 (the default), the distribution reduces to the classic beta distribution (in regression parameterization) without boundary observations.

Value

dxbeta gives the density, pxbeta gives the distribution function, qxbeta gives the quantile function, and rxbeta generates random deviates.