VGAM (version 1.1-9)

Zanegbin: Zero-Altered Negative Binomial Distribution

Description

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

Usage

dzanegbin(x, size, munb, pobs0 = 0, log = FALSE)
pzanegbin(q, size, munb, pobs0 = 0)
qzanegbin(p, size, munb, pobs0 = 0)
rzanegbin(n, size, munb, pobs0 = 0)

Value

dzanegbin gives the density and

pzanegbin gives the distribution function,

qzanegbin gives the quantile function, and

rzanegbin generates random deviates.

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, munb, log

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

pobs0

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

Author

T. W. Yee

Details

The probability function of \(Y\) is 0 with probability pobs0, else a positive negative binomial(\(\mu_{nb}\), size) distribution.

See Also

Gaitdnbinom, zanegbinomial.

Examples

munb <- 3; size <- 4; pobs0 <- 0.3; x <- (-1):7
dzanegbin(x, munb = munb, size = size, pobs0 = pobs0)
table(rzanegbin(100, munb = munb, size = size, pobs0 = pobs0))

if (FALSE)  x <- 0:10
barplot(rbind(dzanegbin(x, munb = munb, size = size, pobs0 = pobs0),
                dnbinom(x, mu   = munb, size = size)),
        beside = TRUE, col = c("blue", "green"), cex.main = 0.7,
        ylab = "Probability", names.arg = as.character(x), las = 1,
        main = paste0("ZANB(munb = ", munb, ", size = ", size,",
               pobs0 = ", pobs0,
               ") [blue] vs",  " NB(mu = ", munb, ", size = ", size,
               ") [green] densities"))