Zipois {VGAM} | R Documentation

## Zero-Inflated Poisson Distribution

### Description

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

### Usage

    dzipois(x, lambda, phi = 0, log = FALSE)
    pzipois(q, lambda, phi = 0)
    qzipois(p, lambda, phi = 0)
    rzipois(n, lambda, phi = 0)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. Must be a single positive integer.
`lambda` | Vector of positive means.
`phi` | Probability of zero (ignoring the Poisson distribution), called phi. The default value of phi=0 corresponds to the response having an ordinary Poisson distribution.
`log` | Logical. Return the logarithm of the answer?

### Details

The probability function of Y is 0 with probability phi, and Poisson(lambda) with probability 1-phi. Thus

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

where W is distributed Poisson(lambda).

### Value

`dzipois` gives the density, `pzipois` gives the distribution function, `qzipois` gives the quantile function, and `rzipois` 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

`dpois`, `zipoisson`, `rzinegbin`.

### Examples

    lambda = 3
    phi = 0.2
    x <- (-1):7
    (i = dzipois(x, lambda, phi))
    max(abs(cumsum(i) - pzipois(x, lambda, phi))) # Should be 0
    table(rzipois(100, lambda, phi))

    table(qzipois(runif(100), lambda, phi))
    round(dzipois(0:10, lambda, phi) * 100) # Should be similar

    ## Not run:
    x = 0:10
    barplot(rbind(dzipois(x, lambda, phi), dpois(x, lambda)),
            beside = TRUE, col = c("blue","green"),
            main=paste("ZIP(", lambda, ", phi=", phi, ") (blue) vs",
                            " Poisson(", lambda, ") (green)", sep=""),
            names.arg = as.character(x))
    ## End(Not run)

[Package VGAM version 0.7-9 Index]