# Zero inflated Poisson inverse Gaussian distributions for fitting a GAMLSS model

### 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

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### Arguments

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

`nu.link` |
Defines the |

`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/)

### See Also

`gamlss.family`

, `PIG`

### Examples

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