betareg

The 4-Parameter Beta Distribution in Regression Parameterization

Description

Density, distribution function, quantile function, and random generation for the 4-parameter beta distribution in regression parameterization.

Usage

dbeta4(x, mu, phi, theta1 = 0, theta2 = 1 - theta1, log = FALSE)

pbeta4(q, mu, phi, theta1 = 0, theta2 = 1 - theta1, lower.tail = TRUE, log.p = FALSE)

qbeta4(p, mu, phi, theta1 = 0, theta2 = 1 - theta1, lower.tail = TRUE, log.p = FALSE)

rbeta4(n, mu, phi, theta1 = 0, theta2 = 1 - theta1)

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 beta distribution that is extended to support [theta1, theta2].
`phi`	numeric. The precision parameter of the beta distribution that is extended to support [theta1, theta2].
`theta1`, `theta2`	numeric. The minimum and maximum, respectively, of the 4-parameter beta distribution. By default a symmetric support is chosen by `theta2 = 1 - theta1` which reduces to the classic beta distribution because of the default `theta1 = 0`.
`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

The distribution is obtained by a linear transformation of a beta-distributed random variable with intercept theta1 and slope theta2 - theta1.

Value

dbeta4 gives the density, pbeta4 gives the distribution function, qbeta4 gives the quantile function, and rbeta4 generates random deviates.