One-inflated beta distribution — oibeta • RTMBdist

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

Usage

doibeta(x, shape1, shape2, oneprob = 0, log = FALSE)

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

roibeta(n, shape1, shape2, oneprob = 0)

Arguments

x, q: vector of quantiles
shape1, shape2: non-negative shape parameters of the beta distribution
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

doibeta gives the density, poibeta gives the distribution function, and roibeta generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

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

Examples

set.seed(123)
x <- roibeta(1, 2, 2, 0.5)
d <- doibeta(x, 2, 2, 0.5)
p <- poibeta(x, 2, 2, 0.5)