The Extended-Support Beta Distribution
dxbeta.RdDensity, 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.