oibeta2: Reparameterised one-inflated beta distribution

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

Reparameterised one-inflated beta distribution

Description

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.

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)].

Value

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

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)

RTMBdist documentation built on Oct. 31, 2026, 5:07 p.m.