# zabinomUC: Zero-Altered Binomial Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2 3 4``` ```dzabinom(x, size, prob, pobs0 = 0, log = FALSE) pzabinom(q, size, prob, pobs0 = 0) qzabinom(p, size, prob, pobs0 = 0) rzabinom(n, size, prob, 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. `size, prob, log` Parameters from the ordinary binomial distribution (see `dbinom`). `pobs0` Probability of (an observed) zero, called pobs0. The default value of `pobs0 = 0` corresponds to the response having a positive binomial distribution.

## Details

The probability function of Y is 0 with probability `pobs0`, else a positive binomial(size, prob) distribution.

## Value

`dzabinom` gives the density and `pzabinom` gives the distribution function, `qzabinom` gives the quantile function, and `rzabinom` 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

`zibinomial`, `Gaitbinom`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```size <- 10; prob <- 0.15; pobs0 <- 0.05; x <- (-1):7 dzabinom(x, size = size, prob = prob, pobs0 = pobs0) table(rzabinom(100, size = size, prob = prob, pobs0 = pobs0)) ## Not run: x <- 0:10 barplot(rbind(dzabinom(x, size = size, prob = prob, pobs0 = pobs0), dbinom(x, size = size, prob = prob)), beside = TRUE, col = c("blue", "orange"), cex.main = 0.7, las = 1, ylab = "Probability", names.arg = as.character(x), main = paste("ZAB(size = ", size, ", prob = ", prob, ", pobs0 = ", pobs0, ") [blue] vs", " Binom(size = ", size, ", prob = ", prob, ") [orange] densities", sep = "")) ## End(Not run) ```

### Example output ```Loading required package: stats4