VGAM (version 0.8-1)

Zanegbin: Zero-Altered Negative Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the zero-altered negative binomial distribution with parameter p0.

Usage

dzanegbin(x, p0, size, prob=NULL, munb=NULL, log = FALSE)
pzanegbin(q, p0, size, prob=NULL, munb=NULL)
qzanegbin(p, p0, size, prob=NULL, munb=NULL)
rzanegbin(n, p0, size, prob=NULL, munb=NULL)

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, munb, log

Parameters from the ordinary negative binomial distribution (see dnbinom). Some arguments have been renamed slightly.

p0

Probability of zero, called $p0$. The default value of p0=0 corresponds to the response having a positive negative binomial distribution.

Value

• dzanegbin gives the density and pzanegbin gives the distribution function, qzanegbin gives the quantile function, and rzanegbin generates random deviates.

Details

The probability function of $Y$ is 0 with probability p0, else a positive $negative binomial(\mu_{nb}, size)$ distribution.

See Also

zanegbinomial, rposnegbin.

Examples

munb = 3; size = 4; p0 = 0.3; x = (-1):7
(ii = dzanegbin(x, p0=p0, munb=munb, size=size))
table(rzanegbin(100, p0=p0, munb=munb, size=size))

x = 0:10
barplot(rbind(dzanegbin(x, p0=p0, munb=munb, size=size),
              dnbinom(x, mu=munb, size=size)),
        beside = TRUE, col = c("blue","green"), cex.main=0.7, las=1,
        ylab = "Probability",names.arg = as.character(x),
        main=paste("ZANB(p0=", p0, ", munb=", munb, ", size=", size,
                   ") [blue] vs", " NB(mu=", munb, ", size=", size,
                   ") [green] densities", sep=""))