Zinegbin {VGAM} | R Documentation

## 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

    dzinegbin(x, phi, size, prob=NULL, munb=NULL, log=FALSE)
    pzinegbin(q, phi, size, prob=NULL, munb=NULL)
    qzinegbin(p, phi, size, prob=NULL, munb=NULL)
    rzinegbin(n, phi, size, prob=NULL, munb=NULL)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. Must be a single positive integer.
`size, prob, munb, log` | Arguments matching `dnbinom`. The argument `munb` corresponds to `mu` in `dnbinom` and has been renamed to emphasize the fact that it is the mean of the negative binomial component.
`phi` | Probability of zero (ignoring the negative binomial distribution), called phi.

### 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.

### Value

`dzinegbin` gives the density, `pzinegbin` gives the distribution function, `qzinegbin` gives the quantile function, and `rzinegbin` 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

`zinegbinomial`, `rnbinom`, `rzipois`.

### Examples

    munb = 3; phi = 0.2; size = k = 10
    x = 0:10
    (i = dzinegbin(x, phi=phi, mu=munb, size=k))
    max(abs(cumsum(i) - pzinegbin(x, phi=phi, mu=munb, size=k))) # Should be 0
    table(rzinegbin(100, phi=phi, mu=munb, size=k))

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

    ## Not run:
    barplot(rbind(dzinegbin(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,
                       ", size=", k, ") (green)", sep=""),
            names.arg = as.character(x))
    ## End(Not run)

[Package VGAM version 0.7-9 Index]