R: Zero-Altered Negative Binomial Distribution

Zanegbin {VGAM} | R Documentation

## 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, prob = NULL, munb = NULL, pobs0 = 0, log = FALSE)
    pzanegbin(q, size, prob = NULL, munb = NULL, pobs0 = 0)
    qzanegbin(p, size, prob = NULL, munb = NULL, pobs0 = 0)
    rzanegbin(n, size, prob = NULL, munb = NULL, 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, 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.

### Details

The probability function of Y is 0 with probability `pobs0`, else a positive negative binomial(munb, size) distribution.

### Value

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

### Note

The argument `pobs0` is recycled to the required length, and must have values which lie in the interval [0,1].

### Author(s)

T. W. Yee

### See Also

`zanegbinomial`, `rposnegbin`.

### 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))

    ## Not run:  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, las = 1,
            ylab = "Probability", names.arg = as.character(x),
            main = paste("ZANB(munb = ", munb, ", size = ", size,",
                         pobs0 = ", pobs0,
                       ") [blue] vs",  " NB(mu = ", munb, ", size = ", size,
                       ") [green] densities", sep = ""))
    ## End(Not run)

[Package VGAM version 1.0-3 Index]