Zero- and one-inflated beta distribution

Density, distribution function, and random generation for the zero-one-inflated beta distribution.

Usage

dzoibeta(x, shape1, shape2, zeroprob = 0, oneprob = 0, log = FALSE)

pzoibeta(q, shape1, shape2, zeroprob = 0, oneprob = 0,
         lower.tail = TRUE, log.p = FALSE)

rzoibeta(n, shape1, shape2, zeroprob = 0, oneprob = 0)

Arguments

x, q

vector of quantiles

shape1, shape2

non-negative shape parameters of the beta distribution

zeroprob

zero-inflation probability between 0 and 1.

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

dzoibeta gives the density, pzoibeta gives the distribution function, and rzoibeta generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

$$f(x;\,a,b,p_0,p_1) = p_0\,\mathbf{1}[x=0] + (1-p_0-p_1)\,f_{\mathrm{Beta}}(x;\,a,b)\,\mathbf{1}[x\in(0,1)] + p_1\,\mathbf{1}[x=1],$$ where \(p_0\) = zeroprob and \(p_1\) = oneprob.

Examples

set.seed(123)
x <- rzoibeta(1, 2, 2, 0.2, 0.3)
d <- dzoibeta(x, 2, 2, 0.2, 0.3)
p <- pzoibeta(x, 2, 2, 0.2, 0.3)