Family Objects for fitting a GAMLSS model

Description Usage Arguments Details Value Note Author(s) References See Also Examples


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


## S3 method for class ''



a gamlss family object e.g. BCT


a gamlss family object e.g. BCT


further arguments passed to or from other methods.


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).


The above GAMLSS families return an object which is of type This object is used to define the family in the gamlss() fit.


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.


Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou


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

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

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,

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




Example output

Loading required package: MASS

GAMLSS Family: NO Normal 
Link function for mu   : log 
Link function for sigma: log 

gamlss.dist documentation built on July 13, 2020, 5:08 p.m.