The Extended-Support Beta Mixture Distribution
dxbetax.RdDensity, 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
unirootandpxbetax.
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.