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 `pstr0`.

### Usage

    dzibinom(x, size, prob, pstr0 = 0, log = FALSE)
    pzibinom(q, size, prob, pstr0 = 0)
    qzibinom(p, size, prob, pstr0 = 0)
    rzibinom(n, size, prob, pstr0 = 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` | Same as in `runif`.

`log` | Same as `pbinom`.
`pstr0` | Probability of a structural zero (i.e., 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 `pstr0` is recycled to the required length, and must have values which lie in the interval [0,1].

These functions actually allow for zero-deflation. That is, the resulting probability of a zero count is less than the nominal value of the parent distribution. See `Zipois` for more information.

### Author(s)

T. W. Yee

### See Also

`zibinomial`, `rgentbinom`, `dbinom`.

### Examples

    prob <- 0.2; size <- 10; pstr0 <- 0.5
    (ii <- dzibinom(0:size, size, prob, pstr0 = pstr0))
    max(abs(cumsum(ii) - pzibinom(0:size, size, prob, pstr0 = pstr0)))  # Should be 0
    table(rzibinom(100, size, prob, pstr0 = pstr0))

    table(qzibinom(runif(100), size, prob, pstr0 = pstr0))
    round(dzibinom(0:10, size, prob, pstr0 = pstr0) * 100)  # Should be similar

    ## Not run:  x <- 0:size
    barplot(rbind(dzibinom(x, size, prob, pstr0 = pstr0),
                    dbinom(x, size, prob)),
            beside = TRUE, col = c("blue", "green"), ylab = "Probability",
            main = paste("ZIB(", size, ", ", prob, ", pstr0 = ", pstr0, ") (blue) vs",
                         " Binomial(", size, ", ", prob, ") (green)", sep=""),
            names.arg = as.character(x), las = 1, lwd = 2)
    ## End(Not run)

[Package VGAM version 1.1-1 Index]