Density, distribution function, quantile function, and random generation for the extended-support beta distribution (in regression parameterization) on [0, 1].
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)
dxbeta gives the density, pxbeta gives the distribution
function, qxbeta gives the quantile function, and rxbeta
generates random deviates.
numeric. Vector of quantiles.
numeric. Vector of probabilities.
numeric. Number of observations. If length(n) > 1, the length is
taken to be the number required.
numeric. The mean of the underlying beta distribution on [-nu, 1 + nu].
numeric. The precision parameter of the underlying beta distribution on [-nu, 1 + nu].
numeric. Exceedence parameter for the support of the underlying beta distribution on [-nu, 1 + nu] that is censored to [0, 1].
logical. If TRUE, probabilities p are given as log(p).
logical. If TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].
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.
dbetar, XBeta