Reparameterised one-inflated beta distribution

Density, distribution function, and random generation for the one-inflated beta distribution reparameterised in terms of mean and concentration.

Usage

doibeta2(x, mu, phi, oneprob = 0, log = FALSE)

poibeta2(q, mu, phi, oneprob = 0, lower.tail = TRUE, log.p = FALSE)

roibeta2(n, mu, phi, oneprob = 0)

Arguments

x, q

vector of quantiles

mu

mean parameter, must be in the interval from 0 to 1.

phi

concentration parameter, must be positive.

oneprob

one-inflation probability between 0 and 1.

log, log.p

logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).

lower.tail

logical; if TRUE, probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

n

number of random values to return.

Value

doibeta2 gives the density, poibeta2 gives the distribution function, and roibeta2 generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

Uses the same density as oibeta with \(a = \mu\phi\) and \(b = (1-\mu)\phi\): $$f(x;\,\mu,\phi,p_1) = p_1\,\mathbf{1}[x=1] + (1-p_1)\,f_{\mathrm{Beta}}(x;\,\mu\phi,\,(1-\mu)\phi)\,\mathbf{1}[x\in(0,1)].$$

Examples

set.seed(123)
x <- roibeta2(1, 0.6, 2, 0.5)
d <- doibeta2(x, 0.6, 2, 0.5)
p <- poibeta2(x, 0.6, 2, 0.5)