Zibinom {VGAM} | R Documentation

## Zero-Inflated Binomial Distribution

### Description

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

### Usage

    dzibinom(x, size, prob, log = FALSE, phi = 0)
    pzibinom(q, size, prob, lower.tail = TRUE, log.p = FALSE, phi = 0)
    qzibinom(p, size, prob, lower.tail = TRUE, log.p = FALSE, phi = 0)
    rzibinom(n, size, prob, phi = 0)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`size` | number of trials. It is the N symbol in the formula given in `zibinomial`.
`prob` | probability of success on each trial.
`n` | number of observations. Must be a single positive integer.
`log, log.p, lower.tail` | Arguments that are passed on to `pbinom`.
`phi` | Probability of zero (ignoring the binomial distribution), called phi. The default value of phi=0 corresponds to the response having an ordinary binomial distribution.

### Details

The probability function of Y is 0 with probability phi, and Binomial(size, prob) with probability 1-phi. Thus

P(Y=0) = phi + (1-phi) * P(W=0)

where W is distributed Binomial(size, prob).

### Value

`dzibinom` gives the density, `pzibinom` gives the distribution function, `qzibinom` gives the quantile function, and `rzibinom` 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

`zibinomial`, `dbinom`.

### Examples

    prob = 0.2; size = 10; phi = 0.5
    (i = dzibinom(0:size, size, prob, phi=phi))
    max(abs(cumsum(i) - pzibinom(0:size, size, prob, phi=phi)))  # Should be 0
    table(rzibinom(100, size, prob, phi=phi))

    table(qzibinom(runif(100), size, prob, phi=phi))
    round(dzibinom(0:10, size, prob, phi=phi) * 100) # Should be similar

    ## Not run:
    x = 0:size
    barplot(rbind(dzibinom(x, size, prob, phi=phi),
                  dbinom(x, size, prob)),
            beside = TRUE, col = c("blue","green"),
            main=paste("ZIB(", size, ", ", prob, ", phi=", phi, ") (blue) vs",
                       " Binomial(", size, ", ", prob, ") (green)", sep=""),
            names.arg = as.character(x), las=1, lwd=2)
    ## End(Not run)

[Package VGAM version 0.7-9 Index]