R: Family Objects for fitting a GAMLSS model

gamlss.family {gamlss.dist} | R Documentation

## Family Objects for fitting a GAMLSS model

### Description

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

### Usage

    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
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` 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 d.stasinopoulos@londonmet.ac.uk, 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.

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. An older version can be found in https://www.gamlss.com/.

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 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, https://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.

### 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

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

[Package gamlss.dist version 5.3-2 Index]