GB2: Generalized Beta Distribution of the Second Kind: Properties, Likelihood, Estimation

Package GB2 explores the Generalized Beta distribution of the second kind. Density, cumulative distribution function, quantiles and moments of the distributions are given. Functions for the full log-likelihood, the profile log-likelihood and the scores are provided. Formulas for various indicators of inequality and poverty under the GB2 are implemented. The GB2 is fitted by the methods of maximum pseudo-likelihood estimation using the full and profile log-likelihood, and non-linear least squares estimation of the model parameters. Various plots for the visualization and analysis of the results are provided. Variance estimation of the parameters is provided for the method of maximum pseudo-likelihood estimation. A mixture distribution based on the compounding property of the GB2 is presented (denoted as "compound" in the documentation). This mixture distribution is based on the discretization of the distribution of the underlying random scale parameter. The discretization can be left or right tail. Density, cumulative distribution function, moments and quantiles for the mixture distribution are provided. The compound mixture distribution is fitted using the method of maximum pseudo-likelihood estimation. The fit can also incorporate the use of auxiliary information. In this new version of the package, the mixture case is complemented with new functions for variance estimation by linearization and comparative density plots.

Install the latest version of this package by entering the following in R:
AuthorMonique Graf <>, Desislava Nedyalkova <>.
Date of publication2015-05-11 23:48:49
MaintainerDesislava Nedyalkova <>
LicenseGPL (>= 2)

View on CRAN

Man pages

Compound: Compound Distribution based on the Generalized Beta...

CompoundAuxDensPlot: Comparison of the compound GB2 and kernel densities by group

CompoundAuxFit: Fitting the Compound Distribution based on the GB2 by the...

CompoundAuxVarest: Variance Estimation under the Compound GB2 Distribution Using...

CompoundDensPlot: Comparison of the GB2, compound GB2 and kernel densities

CompoundFit: Fitting the Compound Distribution based on the GB2 by the...

CompoundIndicators: Indicators of Poverty and Social Exclusion under the Compound...

CompoundMoments: Moments of the Compound Distribution based on the GB2

CompoundQuantiles: Quantiles and random generation of the Compound Distribution...

CompoundVarest: Variance Estimation of the Compound GB2 Distribution

Contindic: Sensitivity Analysis of Laeken Indicators on GB2 Parameters

Contprof: Contour Plot of the Profile Log-likelihood of the GB2...

Fisk: Parameters of the Fisk Distribution

gb2: The Generalized Beta Distribution of the Second Kind

Gini: Computation of the Gini Coefficient for the GB2 Distribution...

Indicators: Monetary Laeken Indicators under the GB2

LogDensity: Log Density of the GB2 Distribution

LogLikelihood: Full Log-likelihood of the GB2 Distribution

MLfitGB2: Fitting the GB2 by the Method of Maximum Likelihood...

MLfullGB2: Maximum Likelihood Estimation of the GB2 Based on the Full...

MLprofGB2: Maximum Likelihood Estimation of the GB2 Based on the Profile...

Moments: Moments and Other Properties of a GB2 Random Variable

NonlinearFit: Fitting the GB2 by Minimizing the Distance Between a Set of...

PlotsML: Cumulative Distribution Plot and Kernel Density Plot for the...

ProfLogLikelihood: Profile Log-likelihood of the GB2 Distribution

RobustWeights: Robustification of the sampling weights

Thomae: Maximum Excess Representation of a Generalized Hypergeometric...

Varest: Variance Estimation of the Parameters of the GB2 Distribution


arpr.cgb2 Man page
arpr.gb2 Man page
arpt.cgb2 Man page
arpt.gb2 Man page
combiopt Man page
Compound Man page
CompoundAuxDensPlot Man page
CompoundAuxFit Man page
CompoundAuxVarest Man page
CompoundDensPlot Man page
CompoundFit Man page
CompoundIndicators Man page
CompoundQuantiles Man page
CompoundVarest Man page
Contindic Man page
contindic.gb2 Man page
Contprof Man page
contprof.gb2 Man page
d2logf.gb2 Man page
dcgb2 Man page
derivind.cgb2 Man page
derivind.gb2 Man page
desvar.cavgb2 Man page
desvar.cgb2 Man page
dgb2 Man page
dl.cgb2 Man page
dlogf.gb2 Man page
dplot.cavgb2 Man page
dplot.cgb2 Man page
el.gb2 Man page
fg.cgb2 Man page
fisk Man page
Fisk Man page
fiskh Man page
gb2 Man page
gb2.gini Man page
Gini Man page
gini.b2 Man page
gini.dag Man page
gini.gb2 Man page Man page
hess.cavgb2 Man page
hess.cgb2 Man page
incompl.cgb2 Man page
incompl.gb2 Man page
Indicators Man page
info.gb2 Man page
kl.gb2 Man page
lambda0.cavgb2 Man page
LogDensity Man page
logf.gb2 Man page
logl.cavgb2 Man page
logl.cgb2 Man page
loglh.gb2 Man page
LogLikelihood Man page
loglp.gb2 Man page
main2.gb2 Man page
main.cgb2 Man page
main.emp Man page
main.gb2 Man page
mkl.cgb2 Man page
ml.cavgb2 Man page
ml.cgb2 Man page
mlfit.gb2 Man page
MLfitGB2 Man page
MLfullGB2 Man page
ml.gb2 Man page
mlh.gb2 Man page
MLprofGB2 Man page
moment.cgb2 Man page
moment.gb2 Man page
Moments Man page
nlsfit.gb2 Man page
NonlinearFit Man page
pcgb2 Man page
pgb2 Man page
pkl.cavgb2 Man page
pl.cgb2 Man page
PlotsML Man page
plotsML.gb2 Man page
pofv.cgb2 Man page
prcgb2 Man page
prof.gb2 Man page
proflogl.gb2 Man page
ProfLogLikelihood Man page
profml.gb2 Man page
profscores.gb2 Man page
qcgb2 Man page
qgb2 Man page
qsr.cgb2 Man page
qsr.gb2 Man page
rcgb2 Man page
rgb2 Man page
rmpg.cgb2 Man page
rmpg.gb2 Man page
RobustWeights Man page
robwts Man page
saveplot Man page
scores.cavgb2 Man page
scores.cgb2 Man page
scoresh.gb2 Man page
scoresp.gb2 Man page
scoreU.cavgb2 Man page
scoreU.cgb2 Man page
scorez.cavgb2 Man page
sl.gb2 Man page
Thomae Man page
ULg Man page
Varest Man page
varscore.cavgb2 Man page
varscore.cgb2 Man page
varscore.gb2 Man page
veind.cavgb2 Man page
veind.cgb2 Man page
veind.gb2 Man page
vepar.cavgb2 Man page
vepar.cgb2 Man page
vepar.gb2 Man page
vl.gb2 Man page
vofp.cgb2 Man page

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