gamlss.family: 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)
"print"(x,...)

Arguments

object

a gamlss family object e.g. BCT

...

further arguments passed to or from other methods.

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.

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	Distributions

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).

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.

Examples

Run this code

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

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