Zapois {VGAM} | R Documentation

## Zero-Altered Poisson Distribution

### Description

Density, distribution function, quantile function and random generation for the zero-altered Poisson distribution with parameter `p0`.

### Usage

    dzapois(x, lambda, p0 = 0, log = FALSE)
    pzapois(q, lambda, p0 = 0)
    qzapois(p, lambda, p0 = 0)
    rzapois(n, lambda, p0 = 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.
`lambda` | Vector of positive means.
`p0` | Probability of zero, called p0. The default value of `p0=0` corresponds to the response having a positive Poisson distribution.
`log` | Logical. Return the logarithm of the answer?

### Details

The probability function of Y is 0 with probability `p0`, else a positive Poisson(lambda).

### Value

`dzapois` gives the density, `pzapois` gives the distribution function, `qzapois` gives the quantile function, and `rzapois` generates random deviates.

### Note

The argument `p0` is recycled to the required length, and must have values which lie in the interval [0,1].

### Author(s)

Thomas W. Yee

### See Also

`zapoisson`.

### Examples

    lambda = 3
    p0 = 0.2
    x = (-1):7
    (i = dzapois(x, lambda, p0))
    max(abs(cumsum(i) - pzapois(x, lambda, p0)))  # Should be 0
    table(rzapois(100, lambda, p0))

    table(qzapois(runif(100), lambda, p0))
    round(dzapois(0:10, lambda, p0) * 100) # Should be similar

    ## Not run:
    x = 0:10
    barplot(rbind(dzapois(x, lambda, p0), dpois(x, lambda)),
            beside = TRUE, col = c("blue","green"),
            main=paste("ZAP(", lambda, ", p0=", p0, ") (blue) vs",
                            " Poisson(", lambda, ") (green)", sep=""),
            names.arg = as.character(x))
    ## End(Not run)

[Package VGAM version 0.7-9 Index]