gamlss.family: Family Objects for fitting a GAMLSS model

In gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape

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, 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, \Sexpr[results=rd]{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, \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1201/b21973")}

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

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

gamlss.dist documentation built on Aug. 24, 2023, 1:06 a.m.