R: Zero inflated and zero adjusted negative binomial...

ZANBI {gamlss.dist} | R Documentation

## Zero inflated and zero adjusted negative binomial distributions for fitting a GAMLSS model

### Description

The function `ZINBI` defines the zero inflated negative binomial distribution, a three parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The functions `dZINBI`, `pZINBI`, `qZINBI` and `rZINBI` define the density, distribution function, quantile function and random generation for the zero inflated negative binomial, `ZINBI()`, distribution.

The function `ZANBI` defines the zero adjusted negative binomial distribution, a three parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The functions `dZANBI`, `pZANBI`, `qZANBI` and `rZANBI` define the density, distribution function, quantile function and random generation for the zero inflated negative binomial, `ZANBI()`, distribution.

### Usage

    ZINBI(mu.link = "log", sigma.link = "log", nu.link = "logit")
    dZINBI(x, mu = 1, sigma = 1, nu = 0.3, log = FALSE)
    pZINBI(q, mu = 1, sigma = 1, nu = 0.3, lower.tail = TRUE, log.p = FALSE)
    qZINBI(p, mu = 1, sigma = 1, nu = 0.3, lower.tail = TRUE, log.p = FALSE)
    rZINBI(n, mu = 1, sigma = 1, nu = 0.3)
    ZANBI(mu.link = "log", sigma.link = "log", nu.link = "logit")
    dZANBI(x, mu = 1, sigma = 1, nu = 0.3, log = FALSE)
    pZANBI(q, mu = 1, sigma = 1, nu = 0.3, lower.tail = TRUE, log.p = FALSE)
    qZANBI(p, mu = 1, sigma = 1, nu = 0.3, lower.tail = TRUE, log.p = FALSE)
    rZANBI(n, mu = 1, sigma = 1, nu = 0.3)

### Arguments

`mu.link` | Defines the `mu.link`, with "log" link as the default for the mu parameter
`sigma.link` | Defines the `sigma.link`, with "log" link as the default for the sigma parameter
`nu.link` | Defines the `mu.link`, with "logit" link as the default for the nu parameter
`x` | vector of (non-negative integer) quantiles
`mu` | vector of positive means
`sigma` | vector of positive despersion parameter
`nu` | vector of zero probability parameter
`p` | vector of probabilities
`q` | vector of quantiles
`n` | number of random values to return
`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]

### Details

The definition for the zero inflated Negative Binomial type I distribution and for the zero adjusted Negative Binomial type I distribution is given in Rigby and Stasinopoulos (2010) below

### Value

The functions `ZINBI` and `ZANBI` return a `gamlss.family` object which can be used to fit a zero inflated or zero adjusted Negative Binomial type I distribution respectively in the `gamlss()` function.

### Author(s)

Mikis Stasinopoulos, Bob Rigby

### References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, https://www.jstatsoft.org/v23/i07.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

### See Also

`gamlss.family`, `NBI`, `NBII`

### Examples

    ZINBI()
    ZANBI()
    # creating data and plotting them
     dat <- rZINBI(1000, mu=5, sigma=.5, nu=0.1)
       r <- barplot(table(dat), col='lightblue')
    dat1 <- rZANBI(1000, mu=5, sigma=.5, nu=0.1)
       r1 <- barplot(table(dat1), col='lightblue')

[Package gamlss.dist version 5.3-2 Index]