# zinbinom: The Zero-inflated Negative Binomial Distribution In AneuFinder: Analysis of Copy Number Variation in Single-Cell-Sequencing 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