# dpqr-zinb: The Zero-Inflated Negative Binomial 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 negative binomial (ZINB) distribution with parameters `k`, `lambda`, and `omega`.

## Usage

 ```1 2 3 4``` ```dzinb(x, k, lambda, omega, log = FALSE) pzinb(q, k, lambda, omega, lower.tail = TRUE, log.p = FALSE) qzinb(p, k, lambda, omega, lower.tail = TRUE, log.p = FALSE) rzinb(n, k, lambda, omega) ```

## Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of random values to return. `k` dispersion parameter. `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

`dzinb` gives the density, `pzinb` gives the distribution function, `qzinb` gives the quantile function, and `rzinb` generates random deviates.

`dzip`, `pzip`, `qzip`, and `rzip` for the zero-inflated Poisson (ZIP) distribution.

## Examples

 ```1 2 3 4 5``` ```dzinb(x = 0:10, k = 1, lambda = 1, omega = 0.5) pzinb(q = c(1, 5, 9), k = 1, lambda = 1, omega = 0.5) qzinb(p = c(0.25, 0.50, 0.75), k = 1, lambda = 1, omega = 0.5) set.seed(123) rzinb(n = 100, k = 1, lambda = 1, omega = 0.5) ```

### Example output

```  0.7500000000 0.1250000000 0.0625000000 0.0312500000 0.0156250000
 0.0078125000 0.0039062500 0.0019531250 0.0009765625 0.0004882813
 0.0002441406
 0.8750000 0.9921875 0.9995117
 0 0 0
 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 4 1 0
 1 1 0 0 1 4 0 1 6 1 2 0 0 0 0 0 1 0 0 0 0 0 3 0 1 0 0 0 1 0 0 0 4 0 0 0 0
 0 2 0 0 3 0 0 0 1 0 1 0 0 0 0 2 0 0 0 0 2 4 0 0 0 0
```

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