# gamlss.family: Family Objects for fitting a GAMLSS model In gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape

## 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. `BCT` `x` a gamlss family object e.g. `BCT` `...` 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 negative binomial `BNB()` 3 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 Double Poisson `DPO()` 2 Double binomial `DBI()` 2 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 Geometric (original) `GEOMo()` 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 Negative Binomial family `NBF()` 3 Normal Exponential t `NET()` 4 (2 fixed) Normal `NO()` 2 Normal Family `NOF()` 3 (1 fixed) Normal Linear Quadratic `LQNO()` 2 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 adjusted beta neg. bin. `ZABNB()` 4 Zero adjusted IG `ZAIG()` 2 Zero adjusted logarithmic `ZALG()` 2 Zero adjusted neg. bin. `ZANBI()` 3 Zero adjusted poisson `ZAP()` 2 Zero adjusted Sichel `ZASICHEL()` 4 Zero adjusted Zipf `ZAZIPF()` 2 Zero inflated binomial `ZIBI()` 2 Zero inflated beta neg. bin. `ZIBNB()` 4 Zero inflated neg. bin. `ZINBI()` 3 Zero inflated poisson `ZIP()` 2 Zero inf. poiss.(mu as mean) `ZIP2()` 2 Zero inflated PIG `ZIPIG()` 3 Zero inflated Sichel `ZISICHEL()` 4 Zipf `ZIPF()` 1

Note that some of the distributions are in the package `gamlss.dist`. The parameters of the distributions are in order, `mu` for location, `sigma` for scale (or dispersion), and `nu` and `tau` for shape. More specifically for the `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 [email protected], 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.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

`BE`,`BB`,`BEINF`,`BI`,`LNO`,`BCT`, `BCPE`,`BCCG`, `GA`,`GU`,`JSU`,`IG`,`LO`, `NBI`,`NBII`,`NO`,`PE`,`PO`, `RG`,`PIG`,`TF`,`WEI`,`WEI2`, `ZIP`
 ```1 2``` ``` normal<-NO(mu.link="log", sigma.link="log") normal ```