R: Distributions for Generalized Additive Models for Location...

gamlss.dist-package {gamlss.dist} | R Documentation

## Distributions for Generalized Additive Models for Location Scale and Shape

### Description

A set of distributions which can be used for modelling the response variables in Generalized Additive Models for Location Scale and Shape, Rigby and Stasinopoulos (2005), <doi:10.1111/j.1467-9876.2005.00510.x>. The distributions can be continuous, discrete or mixed distributions. Extra distributions can be created, by transforming, any continuous distribution defined on the real line, to a distribution defined on ranges 0 to infinity or 0 to 1, by using a ”log” or a ”logit' transformation respectively.

### Details

The DESCRIPTION file:

Package: | gamlss.dist
Type: | Package
Title: | Distributions for Generalized Additive Models for Location Scale and Shape
Version: | 5.3-2
Date: | 2021-03-08
Authors@R: | c(person("Mikis", "Stasinopoulos", role = c("aut", "cre", "cph"), email = "d.stasinopoulos@londonmet.ac.uk"), person("Robert", "Rigby", role = c("aut"), email = "r.rigby@londonmet.ac.uk"), person("Calliope", "Akantziliotou", role = "ctb"), person("Vlasios", "Voudouris", role = "ctb"), person("Gillian", "Heller", role = "ctb"), person("Fernanda", "De Bastiani", role = "ctb"), person("Raydonal", "Ospina", role = "ctb", email= "rospina@ime.usp.br"), person("Nicoletta", "Motpan", role = "ctb"), person("Fiona", "McElduff", role = "ctb"), person("Majid", "Djennad", role = "ctb"), person("Marco", "Enea", role = "ctb"), person("Alexios", "Ghalanos", role = "ctb"), person("Christos", "Argyropoulos", role = "ctb"), person("Almond", "Stocker", role = "ctb"), person("Jens", "Lichter", role = "ctb"), person("Stanislaus", "Stadlmann", role = "ctb") )
Description: | A set of distributions which can be used for modelling the response variables in Generalized Additive Models for Location Scale and Shape, Rigby and Stasinopoulos (2005), <doi:10.1111/j.1467-9876.2005.00510.x>. The distributions can be continuous, discrete or mixed distributions. Extra distributions can be created, by transforming, any continuous distribution defined on the real line, to a distribution defined on ranges 0 to infinity or 0 to 1, by using a ''log'' or a ''logit' transformation respectively.
License: | GPL-2 | GPL-3
URL: | https://www.gamlss.com/
Depends: | R (>= 2.15.0), MASS, graphics, stats, methods, grDevices
Repository: | CRAN
Author: | Mikis Stasinopoulos [aut, cre, cph], Robert Rigby [aut], Calliope Akantziliotou [ctb], Vlasios Voudouris [ctb], Gillian Heller [ctb], Fernanda De Bastiani [ctb], Raydonal Ospina [ctb], Nicoletta Motpan [ctb], Fiona McElduff [ctb], Majid Djennad [ctb], Marco Enea [ctb], Alexios Ghalanos [ctb], Christos Argyropoulos [ctb], Almond Stocker [ctb], Jens Lichter [ctb], Stanislaus Stadlmann [ctb]
Maintainer: | Mikis Stasinopoulos <d.stasinopoulos@londonmet.ac.uk>

Index of help topics:

    BB                      Beta Binomial Distribution For Fitting a GAMLSS
                            Model
    BCCG                    Box-Cox Cole and Green distribution (or Box-Cox
                            normal) for fitting a GAMLSS
    BCPE                    Box-Cox Power Exponential distribution for
                            fitting a GAMLSS
    BCT                     Box-Cox t distribution for fitting a GAMLSS
    BE                      The beta distribution for fitting a GAMLSS
    BEINF                   The beta inflated distribution for fitting a
                            GAMLSS
    BEOI                    The one-inflated beta distribution for fitting
                            a GAMLSS
    BEZI                    The zero-inflated beta distribution for fitting
                            a GAMLSS
    BI                      Binomial distribution for fitting a GAMLSS
    BNB                     Beta Negative Binomial distribution for fitting
                            a GAMLSS
    DBI                     The Double binomial distribution
    DBURR12                 The Discrete Burr type XII distribution for
                            fitting a GAMLSS model
    DEL                     The Delaporte distribution for fitting a GAMLSS
                            model
    DPO                     The Double Poisson distribution
    EGB2                    The exponential generalized Beta type 2
                            distribution for fitting a GAMLSS
    EXP                     Exponential distribution for fitting a GAMLSS
    GA                      Gamma distribution for fitting a GAMLSS
    GAF                     The Gamma distribution family
    GB1                     The generalized Beta type 1 distribution for
                            fitting a GAMLSS
    GB2                     The generalized Beta type 2 and generalized
                            Pareto distributions for fitting a GAMLSS
    GEOM                    Geometric distribution for fitting a GAMLSS
                            model
    GG                      Generalized Gamma distribution for fitting a
                            GAMLSS
    GIG                     Generalized Inverse Gaussian distribution for
                            fitting a GAMLSS
    GPO                     The generalised Poisson distribution
    GT                      The generalized t distribution for fitting a
                            GAMLSS
    GU                      The Gumbel distribution for fitting a GAMLSS
    IG                      Inverse Gaussian distribution for fitting a
                            GAMLSS
    IGAMMA                  Inverse Gamma distribution for fitting a GAMLSS
    JSU                     The Johnson's Su distribution for fitting a
                            GAMLSS
    JSUo                    The original Johnson's Su distribution for
                            fitting a GAMLSS
    LG                      Logarithmic and zero adjusted logarithmic
                            distributions for fitting a GAMLSS model
    LNO                     Log Normal distribution for fitting in GAMLSS
    LO                      Logistic distribution for fitting a GAMLSS
    LOGITNO                 Logit Normal distribution for fitting in GAMLSS
    LQNO                    Normal distribution with a specific mean and
                            variance relationship for fitting a GAMLSS
                            model
    MN3                     Multinomial distribution in GAMLSS
    NBF                     Negative Binomial Family distribution for
                            fitting a GAMLSS
    NBI                     Negative Binomial type I distribution for
                            fitting a GAMLSS
    NBII                    Negative Binomial type II distribution for
                            fitting a GAMLSS
    NET                     Normal Exponential t distribution (NET) for
                            fitting a GAMLSS
    NO                      Normal distribution for fitting a GAMLSS
    NO2                     Normal distribution (with variance as sigma
                            parameter) for fitting a GAMLSS
    NOF                     Normal distribution family for fitting a GAMLSS
    PARETO2                 Pareto distributions for fitting in GAMLSS
    PE                      Power Exponential distribution for fitting a
                            GAMLSS
    PIG                     The Poisson-inverse Gaussian distribution for
                            fitting a GAMLSS model
    PO                      Poisson distribution for fitting a GAMLSS model
    RG                      The Reverse Gumbel distribution for fitting a
                            GAMLSS
    RGE                     Reverse generalized extreme family distribution
                            for fitting a GAMLSS
    SEP                     The Skew Power exponential (SEP) distribution
                            for fitting a GAMLSS
    SEP1                    The Skew Power exponential type 1-4
                            distribution for fitting a GAMLSS
    SHASH                   The Sinh-Arcsinh (SHASH) distribution for
                            fitting a GAMLSS
    SI                      The Sichel dustribution for fitting a GAMLSS
                            model
    SICHEL                  The Sichel distribution for fitting a GAMLSS
                            model
    SIMPLEX                 The simplex distribution for fitting a GAMLSS
    SN1                     Skew Normal Type 1 distribution for fitting a
                            GAMLSS
    SN2                     Skew Normal Type 2 distribution for fitting a
                            GAMLSS
    ST1                     The skew t distributions, type 1 to 5
    TF                      t family distribution for fitting a GAMLSS
    WARING                  Waring distribution for fitting a GAMLSS model
    WEI                     Weibull distribution for fitting a GAMLSS
    WEI2                    A specific parameterization of the Weibull
                            distribution for fitting a GAMLSS
    WEI3                    A specific parameterization of the Weibull
                            distribution for fitting a GAMLSS
    YULE                    Yule distribution for fitting a GAMLSS model
    ZABB                    Zero inflated and zero adjusted Binomial
                            distribution for fitting in GAMLSS
    ZABI                    Zero inflated and zero adjusted Binomial
                            distribution for fitting in GAMLSS
    ZAGA                    The zero adjusted Gamma distribution for
                            fitting a GAMLSS model
    ZAIG                    The zero adjusted Inverse Gaussian distribution
                            for fitting a GAMLSS model
    ZANBI                   Zero inflated and zero adjusted negative
                            binomial distributions for fitting a GAMLSS
                            model
    ZAP                     Zero adjusted poisson distribution for fitting
                            a GAMLSS model
    ZIP                     Zero inflated poisson distribution for fitting
                            a GAMLSS model
    ZIP2                    Zero inflated poisson distribution for fitting
                            a GAMLSS model
    ZIPF                    The zipf and zero adjusted zipf distributions
                            for fitting a GAMLSS model
    checklink               Set the Right Link Function for Specified
                            Parameter and Distribution
    count_1_31              A set of functions to plot gamlss.family
                            distributions
    exGAUS                  The ex-Gaussian distribution
    flexDist                Non-parametric pdf from limited information
                            data
    gamlss.dist-package     Distributions for Generalized Additive Models
                            for Location Scale and Shape
    gamlss.family           Family Objects for fitting a GAMLSS model
    gen.Family              Functions to generate log and logit
                            distributions from existing continuous
                            gamlss.family distributions
    hazardFun               Hazard functions for gamlss.family
                            distributions
    make.link.gamlss        Create a Link for GAMLSS families
    momentSK                Sample and theoretical Moment and Centile
                            Skewness and Kurtosis Functions

### Author(s)

Mikis Stasinopoulos [aut, cre, cph], Robert Rigby [aut], Calliope Akantziliotou [ctb], Vlasios Voudouris [ctb], Gillian Heller [ctb], Fernanda De Bastiani [ctb], Raydonal Ospina [ctb], Nicoletta Motpan [ctb], Fiona McElduff [ctb], Majid Djennad [ctb], Marco Enea [ctb], Alexios Ghalanos [ctb], Christos Argyropoulos [ctb], Almond Stocker [ctb], Jens Lichter [ctb], Stanislaus Stadlmann [ctb]

Maintainer: Mikis Stasinopoulos <d.stasinopoulos@londonmet.ac.uk>

### 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., and De Bastiani F., (2019) Distributions for modelling Location, Scale, and Shape: Using GAMLSS in R, Chapman and Hall/CRC.

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, https://www.jstatsoft.org/v23/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.

### See Also

`gamlss.family`

### Examples

    # pdf plot
    plot(function(y) dSICHEL(y, mu=10, sigma = 0.1 , nu=1 ),
                  from=0, to=30, n=30+1, type="h")
    # cdf plot
    PPP <- par(mfrow=c(2,1))
    plot(function(y) pSICHEL(y, mu=10, sigma =0.1, nu=1 ),
                 from=0, to=30, n=30+1, type="h") # cdf
    cdf<-pSICHEL(0:30, mu=10, sigma=0.1, nu=1)
    sfun1  <- stepfun(1:30, cdf, f = 0)
    plot(sfun1, xlim=c(0,30), main="cdf(x)")
    par(PPP)

[Package gamlss.dist version 5.3-2 Index]