Zibinom {VGAM}R Documentation

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.
p 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.
n 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.

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).

Value

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

Note

The argument phi is recycled to the required length, and must have values which lie in the interval [0,1].

Author(s)

Thomas W. Yee

See Also

zibinomial, dbinom.

Examples

prob = 0.2; size = 10; phi = 0.5
(i = dzibinom(0:size, size, prob, phi=phi))
cumsum(i) - pzibinom(0:size, size, prob, phi=phi)  # Should be 0s
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

## Not run: 
x = 0:size
barplot(rbind(dzibinom(x, size, prob, phi=phi),
              dbinom(x, size, prob)),
        beside = TRUE, col = c("blue","green"),
        main=paste("ZIB(", size, ", ", prob, ", phi=", phi, ") (blue) vs",
                   " Binomial(", size, ", ", prob, ") (green)", sep=""),
        names.arg = as.character(x), las=1, lwd=2)
## End(Not run)

[Package VGAM version 0.7-7 Index]