VGAM (version 0.8-7)

Zabinom: Zero-Altered Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the zero-altered binomial distribution with parameter pobs0.

Usage

dzabinom(x, size, prob, pobs0 = 0, log = FALSE)
pzabinom(q, size, prob, pobs0 = 0)
qzabinom(p, size, prob, pobs0 = 0)
rzabinom(n, size, prob, pobs0 = 0)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1 then the length is taken to be the number required.

size, prob, log

Parameters from the ordinary binomial distribution (see dbinom).

pobs0

Probability of (an observed) zero, called $pobs0$. The default value of pobs0 = 0 corresponds to the response having a positive binomial distribution.

Value

• dzabinom gives the density and pzabinom gives the distribution function, qzabinom gives the quantile function, and rzabinom generates random deviates.

Details

The probability function of $Y$ is 0 with probability pobs0, else a positive binomial(size, prob) distribution.

See Also

zibinomial, rposbinom.

Examples

size <- 10; prob = 0.15; pobs0 <- 0.05; x <- (-1):7
dzabinom(x, size = size, prob = prob, pobs0 = pobs0)
table(rzabinom(100, size = size, prob = prob, pobs0 = pobs0))

x = 0:10
barplot(rbind(dzabinom(x, size = size, prob = prob, pobs0 = pobs0),
                dbinom(x, size = size, prob = prob)),
        beside = TRUE, col = c("blue", "orange"), cex.main = 0.7, las = 1,
        ylab = "Probability", names.arg = as.character(x),
        main = paste("ZAB(size = ", size, ", prob = ", prob, ", pobs0 = ", pobs0,
                   ") [blue] vs",  " Binom(size = ", size, ", prob = ", prob,
                   ") [orange] densities", sep = ""))