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

function.

```
gamlss.family(object,...)
as.gamlss.family(object)
as.family(object)
# S3 method for gamlss.family
print(x,...)
```

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.

- object
a gamlss family object e.g.

`BCT`

- x
a gamlss family object e.g.

`BCT`

- ...
further arguments passed to or from other methods.

Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou

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 |

Discrete Burr XII | `DBURR12()` | 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 |

Logit-Normal | `LOGITNO()` | 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 |

Simplex | `SIMPLEX()` | 2 |

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`

`nu`

`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).

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.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019)
*Distributions for modeling location, scale, and shape: Using GAMLSS in R*, Chapman and Hall/CRC, tools:::Rd_expr_doi("10.1201/9780429298547"). An older version can be found in https://www.gamlss.com/.

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, tools:::Rd_expr_doi("10.18637/jss.v023.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. tools:::Rd_expr_doi("10.1201/b21973")

(see also https://www.gamlss.com/).

`BE`

,`BB`

,`BEINF`

,`BI`

,`LNO`

,`BCT`

,
`BCPE`

,`BCCG`

,
`GA`

,`GU`

,`JSU`

,`IG`

,`LO`

,
`NBI`

,`NBII`

,`NO`

,`PE`

,`PO`

,
`RG`

,`PIG`

,`TF`

,`WEI`

,`WEI2`

,
`ZIP`

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

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