Zero-inflated and reparameterised negative binomial distribution

Probability mass function, distribution function, quantile function and random generation for the zero-inflated negative binomial distribution reparameterised in terms of mean and size.

Usage

dzinbinom2(x, mu, size, zeroprob = 0, log = FALSE)

pzinbinom2(q, mu, size, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzinbinom2(n, mu, size, zeroprob = 0)

Arguments

x, q

vector of (non-negative integer) quantiles

mu

mean parameter, must be positive.

size

size 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, probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

n

number of random values to return.

p

vector of probabilities

Value

dzinbinom2 gives the density, pzinbinom2 gives the distribution function, and rzinbinom2 generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

Uses the same density as zinbinom with \(p = r/(r+\mu)\): $$P(X=k;\,\mu,r,p_0) = p_0\,\mathbf{1}[k=0] + (1-p_0)\,P_{\mathrm{NB}}\!\left(k;\,r,\tfrac{r}{r+\mu}\right).$$

Examples

set.seed(123)
x <- rzinbinom2(1, 2, 1, zeroprob = 0.5)
d <- dzinbinom2(x, 2, 1, zeroprob = 0.5)
p <- pzinbinom2(x, 2, 1, zeroprob = 0.5)