Create an Extended-Support Beta Mixture Distribution
Description
Class and methods for extended-support beta distributions using the workflow from the distributions3 package.
Usage
XBetaX(mu, phi, nu = 0)
Arguments
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].
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.
## all methods above can either be applied elementwise or for## all combinations of X and x, if length(X) = length(x),## also the result can be assured to be a matrix via drop = FALSEp<-c(0.05, 0.5, 0.95)quantile(X, p, elementwise =FALSE)