# ZIPIG: Zero inflated Poisson inverse Gaussian distributions for... In gamlss.dist: Distributions to be Used for GAMLSS Modelling

### Description

The function `ZIPIG` defines the zero inflated Poisson inverse Gaussian distribution, a three parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The functions `dZIPIG`, `pZIPIG`, `qZIPIG` and `rZIPIG` define the density, distribution function, quantile function and random generation for the zero inflated negative binomial, `ZIPIG()`, distribution.

### Usage

 ```1 2 3 4 5``` ```ZIPIG(mu.link = "log", sigma.link = "log", nu.link = "logit") dZIPIG(x, mu = 1, sigma = 1, nu = 0.3, log = FALSE) pZIPIG(q, mu = 1, sigma = 1, nu = 0.3, lower.tail = TRUE, log.p = FALSE) qZIPIG(p, mu = 1, sigma = 1, nu = 0.3, lower.tail = TRUE, log.p = FALSE) rZIPIG(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

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

### Value

The function `ZIPIG` return a `gamlss.family` object which can be used to fit a zero inflated Poisson inverse Gaussian 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/)

`gamlss.family`, `PIG`

### Examples

 ```1 2 3 4 5``` ```ZIPIG() # creating data and plotting them dat <- rZIPIG(1000, mu=5, sigma=.5, nu=0.1) r <- barplot(table(dat), col='lightblue') ```

gamlss.dist documentation built on May 19, 2017, 1:16 p.m.

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