R: Zero inflated poisson distribution for fitting a GAMLSS model

ZIP {gamlss.dist} | R Documentation

## Zero inflated poisson distribution for fitting a GAMLSS model

### Description

The function `ZIP` defines the zero inflated Poisson distribution, a two parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The functions `dZIP`, `pZIP`, `qZIP` and `rZIP` define the density, distribution function, quantile function and random generation for the inflated poisson, `ZIP()`, distribution.

### Usage

    ZIP(mu.link = "log", sigma.link = "logit")
    dZIP(x, mu = 5, sigma = 0.1, log = FALSE)
    pZIP(q, mu = 5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
    qZIP(p, mu = 5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
    rZIP(n, mu = 5, sigma = 0.1)

### Arguments

`mu.link` | defines the `mu.link`, with "log" link as the default for the `mu` parameter
`sigma.link` | defines the `sigma.link`, with "logit" link as the default for the sigma parameter which in this case is the probability at zero. Other links are "probit" and "cloglog"'(complementary log-log)
`x` | vector of (non-negative integer) quantiles
`mu` | vector of positive means
`sigma` | vector of probabilities at zero
`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

Let Y=0 with probability σ and Y \sim Po(μ) with probability (1-σ) the Y has a Zero inflated Poisson Distribution given by

sigma+(1-sigma)e^(-mu)

if (y=0)

f(y)=(1-sigma)e^-mu mu^y/y!

if (y>0) for y=0,1,...,.

### Value

returns a `gamlss.family` object which can be used to fit a zero inflated poisson distribution in the `gamlss()` function.

### Author(s)

Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby

### References

Lambert, D. (1992), Zero-inflated Poisson Regression with an application to defects in Manufacturing, Technometrics, 34, pp 1-14.

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.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

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, http://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`, `PO`, `ZIP2`

### Examples

    ZIP()# gives information about the default links for the normal distribution
    # creating data and plotting them
    dat<-rZIP(1000, mu=5, sigma=.1)
    r <- barplot(table(dat), col='lightblue')
    # library(gamlss)
    # fit the distribution
    # mod1<-gamlss(dat~1, family=ZIP)# fits a constant for mu and sigma
    # fitted(mod1)[1]
    # fitted(mod1,"sigma")[1]

[Package gamlss.dist version 5.0-2 Index]