VGAM (version 0.7-5)

Zinb: Zero-Inflated Negative Binomial Distribution

Description

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

Usage

dzinb(x, phi, size, prob, munb, log.arg=FALSE)
pzinb(q, phi, size, prob, munb)
qzinb(p, phi, size, prob, munb)
rzinb(n, phi, size, prob, munb)

Value

• dzinb gives the density, pzinb gives the distribution function, qzinb gives the quantile function, and rzinb generates random deviates.

Details

The probability function of $Y$ is 0 with probability $\phi$, and a negative binomial distribution with probability $1-\phi$. Thus $$P(Y=0) =\phi + (1-\phi) P(W=0)$$ where $W$ is distributed as a negative binomial distribution (see rnbinom.) See negbinomial, a VGAM family function, for the formula of the probability density function and other details of the negative binomial distribution.

See Also

zinegbinomial, rnbinom, rzipois.

Examples

munb = 3; phi = 0.2; k = 10
x = 0:10
(i = dzinb(x, phi=phi, mu=munb, size=k))
cumsum(i) - pzinb(x, phi=phi, mu=munb, size=k)  # Should be 0s
table(rzinb(100, phi=phi, mu=munb, size=k))

table(qzinb(runif(1000), phi=phi, mu=munb, size=k))
round(dzinb(x, phi=phi, mu=munb, size=k) * 1000) # Should be similar

barplot(rbind(dzinb(x, phi=phi, mu=munb, size=k),
              dnbinom(x, mu=munb, size=k)),
        beside = TRUE, col = c("blue","green"),
        main=paste("ZINB(mu=", munb, ", k=", k, ", phi=", phi,
                   ") (blue) vs negative binomial(mu=", munb,
                   ", k=", k, ") (green)", sep=""),
        names.arg = as.character(x))