Reparameterised zero-inflated beta distribution

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

Usage

dzibeta2(x, mu, phi, zeroprob = 0, log = FALSE)

pzibeta2(q, mu, phi, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzibeta2(n, mu, phi, zeroprob = 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.

zeroprob

zero-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 (default), probabilities are \(P[X \le x]\), otherwise \(P[X > x]\).

n

number of random values to return.

p

vector of probabilities

Value

dzibeta2 gives the density, pzibeta2 gives the distribution function, and rzibeta2 generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

Uses the same density as zibeta with \(a = \mu\phi\) and \(b = (1-\mu)\phi\): $$f(x;\,\mu,\phi,p_0) = p_0\,\mathbf{1}[x=0] + (1-p_0)\,f_{\mathrm{Beta}}(x;\,\mu\phi,\,(1-\mu)\phi)\,\mathbf{1}[x\in(0,1)].$$

Because the continuous part places no mass at zero, zeroprob is exactly \(P(X = 0)\), and zero-inflation coincides with a hurdle model here. The two constructions only differ for discrete distributions, where the base distribution can generate zeros of its own. GAMLSS therefore calls distributions of this type zero-adjusted rather than zero-inflated.

Examples

set.seed(123)
x <- rzibeta2(1, 0.5, 1, 0.5)
d <- dzibeta2(x, 0.5, 1, 0.5)
p <- pzibeta2(x, 0.5, 1, 0.5)