Zero-inflated binomial distribution

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

Usage

dzibinom(x, size, prob, zeroprob = 0, log = FALSE)

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

rzibinom(n, size, prob, zeroprob = 0)

Arguments

x, q

vector of quantiles

size

number of trials (zero or more).

prob

probability of success on each trial.

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

dzibinom gives the probability mass function, pzibinom gives the distribution function, and rzibinom generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

$$P(X=k;\,n,p,p_0) = p_0\,\mathbf{1}[k=0] + (1-p_0)\,P_{\mathrm{Bin}}(k;\,n,p),$$ where \(p_0\) is zeroprob.

Examples

set.seed(123)
x <- rzibinom(1, size = 10, prob = 0.5, zeroprob = 0.5)
d <- dzibinom(x, size = 10, prob = 0.5, zeroprob = 0.5)
p <- pzibinom(x, size = 10, prob = 0.5, zeroprob = 0.5)