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gamlss.dist (version 6.1-1)

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

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.

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.

Author

Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou

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.

DistributionsR namesNo of parameters
BetaBE()2
Beta BinomialBB()2
Beta negative binomialBNB()3
Beta one inflatedBEOI()3
Beta zero inflatedBEZI()3
Beta inflatedBEINF()4
BinomialBI()1
Box-Cox Cole and GreenBCCG()3
Box-Cox Power ExponentialBCPE()4
Box-Cox-tBCT()4
DelaportDEL()3
Discrete Burr XIIDBURR12()3
Double PoissonDPO()2
Double binomialDBI()2
ExponentialEXP()1
Exponential GaussianexGAUS()3
Exponential generalized Beta type 2EGB2()4
GammaGA()2
Generalized Beta type 1GB1()4
Generalized Beta type 2GB2()4
Generalized GammaGG()3
Generalized Inverse GaussianGIG()3
Generalized tGT()4
GeometricGEOM()1
Geometric (original)GEOMo()1
GumbelGU()2
Inverse GammaIGAMMA()2
Inverse GaussianIG()2
Johnson's SUJSU()4
LogarithmicLG()1
LogisticLO()2
Logit-NormalLOGITNO()2
log-NormalLOGNO()2
log-Normal (Box-Cox)LNO()3 (1 fixed)
Negative Binomial type INBI()2
Negative Binomial type IINBII()2
Negative Binomial familyNBF()3
Normal Exponential tNET()4 (2 fixed)
NormalNO()2
Normal FamilyNOF()3 (1 fixed)
Normal Linear QuadraticLQNO()2
Pareto type 2PARETO2()2
Pareto type 2 originalPARETO2o()2
Power ExponentialPE()3
Power Exponential type 2PE2()3
PoisonPO()1
Poisson inverse GaussianPIG()2
Reverse generalized extremeRGE()3
Reverse GumbelRG()2
Skew Power Exponential type 1SEP1()4
Skew Power Exponential type 2SEP2()4
Skew Power Exponential type 3SEP3()4
Skew Power Exponential type 4SEP4()4
ShashSHASH()4
Shash originalSHASHo()4
Shash original 2SHASH()4
Sichel (original)SI()3
Sichel (mu as the maen)SICHEL()3
SimplexSIMPLEX()2
Skew t type 1ST1()3
Skew t type 2ST2()3
Skew t type 3ST3()3
Skew t type 4ST4()3
Skew t type 5ST5()3
t-distributionTF()3
WaringWARING()1
WeibullWEI()2
Weibull(PH parameterization)WEI2()2
Weibull (mu as mean)WEI3()2
YuleYULE()1
Zero adjusted binomialZABI()2
Zero adjusted beta neg. bin.ZABNB()4
Zero adjusted IGZAIG()2
Zero adjusted logarithmicZALG()2
Zero adjusted neg. bin.ZANBI()3
Zero adjusted poissonZAP()2
Zero adjusted SichelZASICHEL()4
Zero adjusted ZipfZAZIPF()2
Zero inflated binomialZIBI()2
Zero inflated beta neg. bin.ZIBNB()4
Zero inflated neg. bin.ZINBI()3
Zero inflated poissonZIP()2
Zero inf. poiss.(mu as mean)ZIP2()2
Zero inflated PIGZIPIG()3
Zero inflated SichelZISICHEL()4
ZipfZIPF()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).

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, 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/).

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

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

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