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.

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`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 |

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*.

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

function.

For the function `IGAMMA()`

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

Fiona McElduff, Bob Rigby and Mikis Stasinopoulos.

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.

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