# Inverse Gamma distribution for fitting a GAMLSS

### Description

The function `IGAMMA()`

defines the Inverse Gamma distribution, a two parameter distribution, for a `gamlss.family`

object to be used in GAMLSS fitting using the function `gamlss()`

, with parameters `mu`

(the mode) and `sigma`

. The functions `dIGAMMA`

, `pIGAMMA`

, `qIGAMMA`

and `rIGAMMA`

define the density, distribution function, quantile function and random generation for the `IGAMMA`

parameterization of the Inverse Gamma distribution.

### Usage

1 2 3 4 5 |

### Arguments

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

`x, q` |
vector of quantiles |

`mu` |
vector of location parameter values |

`sigma` |
vector of scale parameter values |

`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] |

`p` |
vector of probabilities |

`n` |
number of observations. If |

### Details

The parameterization of the Inverse Gamma distribution in the function `IGAMMA`

is

*f(y|mu, sigma) = ([mu (alpha+1)]^alpha)/Gamma(alpha) y^(-(alpha+1)) exp(-(mu (alpha+1))/y)*

where *alpha = 1/(sigma^2)*
for *y>0*, *mu>0* and *sigma>0*.

### Value

returns a gamlss.family object which can be used to fit an Inverse Gamma distribution in the `gamlss()`

function.

### Note

For the function `IGAMMA()`

, *mu* is the mode of the Inverse Gamma distribution.

### Author(s)

Fiona McElduff, Bob Rigby and Mikis Stasinopoulos.

### 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.

### See Also

`gamlss.family`

, `GA`

### Examples

1 2 3 4 5 6 7 8 9 10 |