Zibinom: Zero-Inflated Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the zero-inflated binomial distribution with parameter phi.

Usage

dzibinom(x, size, prob, log = FALSE, phi = 0)
pzibinom(q, size, prob, lower.tail = TRUE, log.p = FALSE, phi = 0)
qzibinom(p, size, prob, lower.tail = TRUE, log.p = FALSE, phi = 0)
rzibinom(n, size, prob, phi = 0)

Arguments

x, q

vector of quantiles.

vector of probabilities.

size

number of trials. It is the $N$ symbol in the formula given in zibinomial.

prob

probability of success on each trial.

number of observations. Must be a single positive integer.

log, log.p, lower.tail

Arguments that are passed on to pbinom.

phi

Probability of zero (ignoring the binomial distribution), called $\phi$. The default value of $\phi=0$ corresponds to the response having an ordinary binomial distribution.

Value

dzibinom gives the density, pzibinom gives the distribution function, qzibinom gives the quantile function, and rzibinom generates random deviates.

Details

The probability function of $Y$ is 0 with probability $\phi$, and $Binomial(size, prob)$ with probability $1-\phi$. Thus $$P(Y=0) =\phi + (1-\phi) P(W=0)$$ where $W$ is distributed $Binomial(size, prob)$.

Examples

Run this code

prob = 0.2; size = 10; phi = 0.5
(ii = dzibinom(0:size, size, prob, phi = phi))
max(abs(cumsum(ii) - pzibinom(0:size, size, prob, phi = phi)))  # Should be 0
table(rzibinom(100, size, prob, phi = phi))

table(qzibinom(runif(100), size, prob, phi = phi))
round(dzibinom(0:10, size, prob, phi = phi) * 100) # Should be similar

x = 0:size
barplot(rbind(dzibinom(x, size, prob, phi = phi),
                dbinom(x, size, prob)),
        beside = TRUE, col = c("blue", "green"), ylab = "Probability",
        main = paste("ZIB(", size, ", ", prob, ", phi = ", phi, ") (blue) vs",
                     " Binomial(", size, ", ", prob, ") (green)", sep=""),
        names.arg = as.character(x), las = 1, lwd = 2)