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 class 'gamlss.family':
print(x,...)
gamlss.family.default(object,...)

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. lll{ 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 Gumbel GU() 2 Inverse Gaussian IG() 2 Johnson's SU JSU() 4 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) 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 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 Weibull WEI() 2 Weibull(PH parameterization) WEI2() 2 Weibull (mu as mean) WEI3() 2 Zero inflated poisson ZIP() 2 Zero inf. poiss.(mu as mean) ZIP2() 2 Zero adjusted IG ZAIG() 2 } 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.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, http://www.jstatsoft.org/v23/i07.

Examples

Run this code

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

Run the code above in your browser using DataLab