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 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
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.
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.
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