# Family Objects for fitting a GAMLSS model

### Description

GAMLSS families are the current available distributions that can be fitted using the `gamlss()`

function.

### Usage

1 2 3 4 5 | ```
gamlss.family(object,...)
as.gamlss.family(object)
as.family(object)
## S3 method for class 'gamlss.family'
print(x,...)
``` |

### Arguments

`object` |
a gamlss family object e.g. |

`x` |
a gamlss family object e.g. |

`...` |
further arguments passed to or from other methods. |

### Details

There are several distributions available for the response variable in the `gamlss`

function.
The following table display their names and their abbreviations in `R`

. Note that the different distributions can be fitted
using their `R`

abbreviations
(and optionally excluding the brackets) i.e. family=BI(), family=BI are equivalent.

Distributions | R names | No of parameters |

Beta | `BE()` | 2 |

Beta Binomial | `BB()` | 2 |

Beta one inflated | `BEOI()` | 3 |

Beta zero inflated | `BEZI()` | 3 |

Beta inflated | `BEINF()` | 4 |

Binomial | `BI()` | 1 |

Box-Cox Cole and Green | `BCCG()` | 3 |

Box-Cox Power Exponential | `BCPE()` | 4 |

Box-Cox-t | `BCT()` | 4 |

Delaport | `DEL()` | 3 |

Exponential | `EXP()` | 1 |

Exponential Gaussian | `exGAUS()` | 3 |

Exponential generalized Beta type 2 | `EGB2()` | 4 |

Gamma | `GA()` | 2 |

Generalized Beta type 1 | `GB1()` | 4 |

Generalized Beta type 2 | `GB2()` | 4 |

Generalized Gamma | `GG()` | 3 |

Generalized Inverse Gaussian | `GIG()` | 3 |

Generalized t | `GT()` | 4 |

Geometric | `GEOM()` | 1 |

Gumbel | `GU()` | 2 |

Inverse Gamma | `IGAMMA()` | 2 |

Inverse Gaussian | `IG()` | 2 |

Johnson's SU | `JSU()` | 4 |

Logarithmic | `LG()` | 1 |

Logistic | `LO()` | 2 |

log-Normal | `LOGNO()` | 2 |

log-Normal (Box-Cox) | `LNO()` | 3 (1 fixed) |

Negative Binomial type I | `NBI()` | 2 |

Negative Binomial type II | `NBII()` | 2 |

Normal Exponential t | `NET()` | 4 (2 fixed) |

Normal | `NO()` | 2 |

Normal Family | `NOF()` | 3 (1 fixed) |

Pareto type 2 | `PARETO2()` | 2 |

Pareto type 2 original | `PARETO2o()` | 2 |

Power Exponential | `PE()` | 3 |

Power Exponential type 2 | `PE2()` | 3 |

Poison | `PO()` | 1 |

Poisson inverse Gaussian | `PIG()` | 2 |

Reverse generalized extreme | `RGE()` | 3 |

Reverse Gumbel | `RG()` | 2 |

Skew Power Exponential type 1 | `SEP1()` | 4 |

Skew Power Exponential type 2 | `SEP2()` | 4 |

Skew Power Exponential type 3 | `SEP3()` | 4 |

Skew Power Exponential type 4 | `SEP4()` | 4 |

Shash | `SHASH()` | 4 |

Shash original | `SHASHo()` | 4 |

Shash original 2 | `SHASH()` | 4 |

Sichel (original) | `SI()` | 3 |

Sichel (mu as the maen) | `SICHEL()` | 3 |

Skew t type 1 | `ST1()` | 3 |

Skew t type 2 | `ST2()` | 3 |

Skew t type 3 | `ST3()` | 3 |

Skew t type 4 | `ST4()` | 3 |

Skew t type 5 | `ST5()` | 3 |

t-distribution | `TF()` | 3 |

Waring | `WARING()` | 1 |

Weibull | `WEI()` | 2 |

Weibull(PH parameterization) | `WEI2()` | 2 |

Weibull (mu as mean) | `WEI3()` | 2 |

Yule | `YULE()` | 1 |

Zero adjusted binomial | `ZABI()` | 2 |

Zero inflated binomial | `ZIBI()` | 2 |

Zero adjusted logarithmic | `ZALG()` | 2 |

Zero inflated poisson | `ZIP()` | 2 |

Zero inf. poiss.(mu as mean) | `ZIP2()` | 2 |

Zero adjusted poisson | `ZAP()` | 2 |

Zero adjusted IG | `ZAIG()` | 2 |

Note that some of the distributions are in the package `gamlss.dist`

.
The parameters of the distributions are in order, ** mu** for location,

**for scale (or dispersion), and**

`sigma`

**and**

`nu`

**for shape. More specifically for the**

`tau`

`BCCG`

family `mu`

is the median, `sigma`

approximately the coefficient of variation, and `nu`

the skewness parameter.
The parameters for `BCPE`

distribution have the same interpretation with the extra fourth parameter `tau`

modelling
the kurtosis of the distribution. The parameters for BCT have the same interpretation except that
*sigma*((tau/(tau-2))^0.5)*is approximately the coefficient of variation.

All of the distribution in the above list are also provided with the corresponding `d`

, `p`

, `q`

and `r`

functions
for density (pdf), distribution function (cdf), quantile function and random generation function respectively, (see individual distribution for details).

### Value

The above GAMLSS families return an object which is of type `gamlss.family`

. This object is used to define the family in the `gamlss()`

fit.

### Note

More distributions will be documented in later GAMLSS releases. Further user defined distributions can be incorporate relatively easy, see, for example, the help documentation accompanying the gamlss library.

### Author(s)

Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby and Calliope Akantziliotou

### 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

`BE`

,`BB`

,`BEINF`

,`BI`

,`LNO`

,`BCT`

,
`BCPE`

,`BCCG`

,
`GA`

,`GU`

,`JSU`

,`IG`

,`LO`

,
`NBI`

,`NBII`

,`NO`

,`PE`

,`PO`

,
`RG`

,`PIG`

,`TF`

,`WEI`

,`WEI2`

,
`ZIP`

### Examples

1 2 | ```
normal<-NO(mu.link="log", sigma.link="log")
normal
``` |