R: The Extended-Support Beta Mixture Distribution

xbetax {betareg}

R Documentation

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