R: Zero adjusted poisson distribution for fitting a GAMLSS model

ZAP {gamlss.dist} | R Documentation

## Zero adjusted poisson distribution for fitting a GAMLSS model

### Description

The function `ZAP` defines the zero adjusted Poisson distribution, a two parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The functions `dZAP`, `pZAP`, `qZAP` and `rZAP` define the density, distribution function, quantile function and random generation for the inflated poisson, `ZAP()`, distribution.

### Usage

    ZAP(mu.link = "log", sigma.link = "logit")
    dZAP(x, mu = 5, sigma = 0.1, log = FALSE)
    pZAP(q, mu = 5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
    qZAP(p, mu = 5, sigma = 0.1, lower.tail = TRUE, log.p = FALSE)
    rZAP(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)
`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

For the definition of the distribution see Rigby and Stasinopoulos (2010) below.

### Value

The function `ZAP` 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

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.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or see http://www.gamlss.org/)

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`, `ZIP`, `ZIP2`, `ZALG`

### Examples

    ZAP()
    # creating data and plotting them
    dat<-rZAP(1000, mu=5, sigma=.1)
    r <- barplot(table(dat), col='lightblue')

[Package gamlss.dist version 5.0-2 Index]