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betareg (version 3.2-1)

xbetax: 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)

Value

dxbetax gives the density, pxbetax gives the distribution function, qxbetax gives the quantile function, and rxbetax

generates random deviates.

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.

See Also

dxbeta, XBetaX