zinbinom {chromstaR} | R Documentation

## The Zero-inflated Negative Binomial Distribution

### Description

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

### Usage

    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

### See Also

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.

[Package chromstaR version 1.20.2 Index]