# zinbinom: The Zero-inflated Negative Binomial Distribution In chromstaR: Combinatorial and Differential Chromatin State Analysis for ChIP-Seq Data

## Description

Density, distribution function, quantile function and random generation for the zero-inflated negative binomial distribution with parameters `w`, `size` and `prob`.

## Usage

 ```1 2 3 4 5 6 7``` ```dzinbinom(x, w, size, prob, mu) pzinbinom(q, w, size, prob, mu, lower.tail = TRUE) qzinbinom(p, w, size, prob, mu, lower.tail = TRUE) rzinbinom(n, w, size, prob, mu) ```

## Arguments

 `x` Vector of (non-negative integer) quantiles. `w` Weight of the zero-inflation. `0 <= w <= 1`. `size` Target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer. `prob` Probability of success in each trial. `0 < prob <= 1`. `mu` Alternative parametrization via mean: see ‘Details’. `q` Vector of quantiles. `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. `p` Vector of probabilities. `n` number of observations. If `length(n) > 1`, the length is taken to be the number required.

## Details

The zero-inflated negative binomial distribution with `size` = n and `prob` = p has density

w + (1-w) * Γ(x+n)/(Γ(n) x!) p^n (1-p)^x

for x = 0, n > 0, 0 < p ≤ 1 and 0 ≤ w ≤ 1.

(1-w) * Γ(x+n)/(Γ(n) x!) p^n (1-p)^x

for x = 1, 2, …, n > 0, 0 < p ≤ 1 and 0 ≤ w ≤ 1.

## Value

dzinbinom gives the density, pzinbinom gives the distribution function, qzinbinom gives the quantile function, and rzinbinom generates random deviates.

## Functions

• `dzinbinom`: gives the density

• `pzinbinom`: gives the cumulative distribution function

• `qzinbinom`: gives the quantile function

• `rzinbinom`: random number generation

## Author(s)

Matthias Heinig, Aaron Taudt

Distributions for standard distributions, including `dbinom` for the binomial, `dnbinom` for the negative binomial, `dpois` for the Poisson and `dgeom` for the geometric distribution, which is a special case of the negative binomial.