Zero-inflated geometric distribution

Probability mass function, distribution function, and random generation for the zero-inflated geometric distribution.

Usage

dzigeom(x, prob, zeroprob = 0, log = FALSE)

pzigeom(q, prob, zeroprob = 0, lower.tail = TRUE, log.p = FALSE)

rzigeom(n, prob, zeroprob = 0)

Arguments

x, q: integer vector of counts
prob: probability of success in each trial, in (0,1]
zeroprob: zero-inflation probability between 0 and 1
log, log.p: logical; return log-density if TRUE
lower.tail: logical; if TRUE, probabilities are $P[X \le x]$, otherwise, $P[X > x]$.
n: number of random values to return.

Value

dzigeom gives the probability mass function, pzigeom gives the distribution function, and rzigeom generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

$$P(X=k;\,\pi,p_0) = p_0\,\mathbf{1}[k=0] + (1-p_0)\,P_{\mathrm{Geom}}(k;\,\pi),$$ where $p_0$ is zeroprob. The zeros are a mixture of structural zeros and zeros generated by the geometric itself, so zeroprob is not the probability of observing a zero; see hgeom for the hurdle version, where it is.

Examples

set.seed(123)
x <- rzigeom(5, prob = 0.3, zeroprob = 0.4)
d <- dzigeom(x, prob = 0.3, zeroprob = 0.4)
p <- pzigeom(x, prob = 0.3, zeroprob = 0.4)