# zapoisUC: Zero-Altered Poisson Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

Density, distribution function, quantile function and random generation for the zero-altered Poisson distribution with parameter `pobs0`.

## Usage

 ```1 2 3 4``` ```dzapois(x, lambda, pobs0 = 0, log = FALSE) pzapois(q, lambda, pobs0 = 0) qzapois(p, lambda, pobs0 = 0) rzapois(n, lambda, pobs0 = 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. `pobs0` Probability of zero, called pobs0. The default value of `pobs0 = 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 `pobs0`, 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 `pobs0` is recycled to the required length, and must have values which lie in the interval [0,1].

## Author(s)

T. W. Yee

`zapoisson`, `Gaitpois`, `dzipois`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```lambda <- 3; pobs0 <- 0.2; x <- (-1):7 (ii <- dzapois(x, lambda, pobs0)) max(abs(cumsum(ii) - pzapois(x, lambda, pobs0))) # Should be 0 table(rzapois(100, lambda, pobs0)) table(qzapois(runif(100), lambda, pobs0)) round(dzapois(0:10, lambda, pobs0) * 100) # Should be similar ## Not run: x <- 0:10 barplot(rbind(dzapois(x, lambda, pobs0), dpois(x, lambda)), beside = TRUE, col = c("blue", "green"), las = 1, main = paste("ZAP(", lambda, ", pobs0 = ", pobs0, ") [blue] vs", " Poisson(", lambda, ") [green] densities", sep = ""), names.arg = as.character(x), ylab = "Probability") ## End(Not run) ```