# dpqr-zip: The Zero-Inflated Poisson Distribution In ZIM: Zero-Inflated Models (ZIM) for Count Time Series with Excess Zeros

## Description

Density, distribution function, quantile function and random generation for the zero-inflated Poisson (ZIP) distribution with parameters `lambda` and `omega`.

## Usage

 ```1 2 3 4``` ```dzip(x, lambda, omega, log = FALSE) pzip(q, lambda, omega, lower.tail = TRUE, log.p = FALSE) qzip(p, lambda, omega, lower.tail = TRUE, log.p = FALSE) rzip(n, lambda, omega) ```

## Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of random values to return. `lambda` vector of (non-negative) means. `omega` zero-inflation parameter. `log, log.p` logical; if TRUE, probabilities `p` are given as `log(p)`. `lower.tail` logical; if TRUE (default), probabilities are `P[X <= x]`, otherwise, `P[X > x]`.

## Value

`dzip` gives the density, `pzip` gives the distribution function, `qzip` gives the quantile function, and `rzip` generates random deviates.

`dzinb`, `pzinb`, `qzinb`, and `rzinb` for the zero-inflated negative binomial (ZINB) distribution.

## Examples

 ```1 2 3 4 5``` ```dzip(x = 0:10, lambda = 1, omega = 0.5) pzip(q = c(1, 5, 9), lambda = 1, omega = 0.5) qzip(p = c(0.25, 0.50, 0.75), lambda = 1, omega = 0.5) set.seed(123) rzip(n = 100, lambda = 1, omega = 0.5) ```

### Example output

``` [1] 6.839397e-01 1.839397e-01 9.196986e-02 3.065662e-02 7.664155e-03
[6] 1.532831e-03 2.554718e-04 3.649598e-05 4.561997e-06 5.068886e-07
[11] 5.068886e-08
[1] 0.8678794 0.9997029 0.9999999
[1] 0 0 1
[1] 1 0 1 0 0 2 0 0 0 0 0 0 0 0 1 0 1 3 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0
[38] 2 3 1 0 1 0 0 2 0 0 0 0 0 2 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 2
[75] 1 1 1 0 2 1 2 0 1 0 1 1 0 0 0 2 0 0 4 0 3 1 0 1 0 0
```

ZIM documentation built on May 2, 2019, 7:01 a.m.