betareg

The Extended-Support Beta Mixture Distribution

Description

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

Usage

dxbetax(x, mu, phi, nu = 0, log = FALSE, quad = 20)

pxbetax(q, mu, phi, nu = 0, lower.tail = TRUE, log.p = FALSE, quad = 20)

qxbetax(p, mu, phi, nu = 0, lower.tail = TRUE, log.p = FALSE, quad = 20,
  tol = .Machine\$double.eps^0.7)

rxbetax(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. Mean of the exponentially-distributed exceedence parameter for 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].
`quad`	numeric. The number of quadrature points for numeric integration of the continuous mixture. Alternatively, a matrix with nodes and weights for the quadrature points can be specified.
`tol`	numeric. Accuracy (convergence tolerance) for numerically determining quantiles based on `uniroot` and `pxbetax`.

Details

The extended-support beta mixture distribution is a continuous mixture of extended-support beta distributions on [0, 1] where the underlying exceedence parameter is exponentially distributed with mean nu. Thus, if nu > 0, the resulting distribution has point masses on the boundaries 0 and 1 with larger values of nu leading to higher boundary probabilities. For nu = 0 (the default), the distribution reduces to the classic beta distribution (in regression parameterization) without boundary observations.

Value

dxbetax gives the density, pxbetax gives the distribution function, qxbetax gives the quantile function, and rxbetax generates random deviates.