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

## Documentation for package ‘GB2’ version 2.1

- DESCRIPTION file.

## Help Pages

A C D E F G H I K L M N P Q R S T U V

## -- A --

arpr.cgb2 | Indicators of Poverty and Social Exclusion under the Compound Distribution based on the GB2
arpr.gb2 | Monetary Laeken Indicators under the GB2
arpt.cgb2 | Indicators of Poverty and Social Exclusion under the Compound Distribution based on the GB2
arpt.gb2 | Monetary Laeken Indicators under the GB2

## -- C --

combiopt | Maximum Excess Representation of a Generalized Hypergeometric Function Using Thomae's Theorem
Compound | Compound Distribution based on the Generalized Beta Distribution of the Second Kind
CompoundAuxDensPlot | Comparison of the compound GB2 and kernel densities by group
CompoundAuxFit | Fitting the Compound Distribution based on the GB2 by the Method of Pseudo Maximum Likelihood Estimation using Auxiliary Information
CompoundAuxVarest | Variance Estimation under the Compound GB2 Distribution Using Auxiliary Information
CompoundDensPlot | Comparison of the GB2, compound GB2 and kernel densities
CompoundFit | Fitting the Compound Distribution based on the GB2 by the Method of Maximum Likelihood Estimation
CompoundIndicators | Indicators of Poverty and Social Exclusion under the Compound Distribution based on the GB2
CompoundQuantiles | Quantiles and random generation of the Compound Distribution based on the GB2
CompoundVarest | Variance Estimation of the Compound GB2 Distribution
Contindic | Sensitivity Analysis of Laeken Indicators on GB2 Parameters
contindic.gb2 | Sensitivity Analysis of Laeken Indicators on GB2 Parameters
Contprof | Contour Plot of the Profile Log-likelihood of the GB2 Distribution
contprof.gb2 | Contour Plot of the Profile Log-likelihood of the GB2 Distribution

## -- D --

d2logf.gb2 | Log Density of the GB2 Distribution
dcgb2 | Compound Distribution based on the Generalized Beta Distribution of the Second Kind
derivind.cgb2 | Variance Estimation of the Compound GB2 Distribution
derivind.gb2 | Variance Estimation of the Parameters of the GB2 Distribution
desvar.cavgb2 | Variance Estimation under the Compound GB2 Distribution Using Auxiliary Information
desvar.cgb2 | Variance Estimation of the Compound GB2 Distribution
dgb2 | The Generalized Beta Distribution of the Second Kind
dl.cgb2 | Compound Distribution based on the Generalized Beta Distribution of the Second Kind
dlogf.gb2 | Log Density of the GB2 Distribution
dplot.cavgb2 | Comparison of the compound GB2 and kernel densities by group
dplot.cgb2 | Comparison of the GB2, compound GB2 and kernel densities

## -- E --

el.gb2 | Moments and Other Properties of a GB2 Random Variable

## -- F --

fg.cgb2 | Compound Distribution based on the Generalized Beta Distribution of the Second Kind
Fisk | Parameters of the Fisk Distribution
fisk | Parameters of the Fisk Distribution
fiskh | Parameters of the Fisk Distribution

## -- G --

gb2 | The Generalized Beta Distribution of the Second Kind
gb2.gini | Maximum Excess Representation of a Generalized Hypergeometric Function Using Thomae's Theorem
Gini | Computation of the Gini Coefficient for the GB2 Distribution and its Particular Cases.
gini.b2 | Computation of the Gini Coefficient for the GB2 Distribution and its Particular Cases.
gini.dag | Computation of the Gini Coefficient for the GB2 Distribution and its Particular Cases.
gini.gb2 | Computation of the Gini Coefficient for the GB2 Distribution and its Particular Cases.
gini.sm | Computation of the Gini Coefficient for the GB2 Distribution and its Particular Cases.

## -- H --

hess.cavgb2 | Variance Estimation under the Compound GB2 Distribution Using Auxiliary Information
hess.cgb2 | Variance Estimation of the Compound GB2 Distribution

## -- I --

incompl.cgb2 | Moments of the Compound Distribution based on the GB2
incompl.gb2 | Moments and Other Properties of a GB2 Random Variable
Indicators | Monetary Laeken Indicators under the GB2
info.gb2 | Full Log-likelihood of the GB2 Distribution

## -- K --

kl.gb2 | Moments and Other Properties of a GB2 Random Variable

## -- L --

lambda0.cavgb2 | Fitting the Compound Distribution based on the GB2 by the Method of Pseudo Maximum Likelihood Estimation using Auxiliary Information
LogDensity | Log Density of the GB2 Distribution
logf.gb2 | Log Density of the GB2 Distribution
logl.cavgb2 | Fitting the Compound Distribution based on the GB2 by the Method of Pseudo Maximum Likelihood Estimation using Auxiliary Information
logl.cgb2 | Fitting the Compound Distribution based on the GB2 by the Method of Maximum Likelihood Estimation
loglh.gb2 | Full Log-likelihood of the GB2 Distribution
LogLikelihood | Full Log-likelihood of the GB2 Distribution
loglp.gb2 | Full Log-likelihood of the GB2 Distribution

## -- M --

main.cgb2 | Indicators of Poverty and Social Exclusion under the Compound Distribution based on the GB2
main.emp | Fitting the GB2 by the Method of Maximum Likelihood Estimation and Comparison of the Fitted Indicators with the Empirical Indicators
main.gb2 | Monetary Laeken Indicators under the GB2
main2.gb2 | Monetary Laeken Indicators under the GB2
mkl.cgb2 | Moments of the Compound Distribution based on the GB2
ml.cavgb2 | Fitting the Compound Distribution based on the GB2 by the Method of Pseudo Maximum Likelihood Estimation using Auxiliary Information
ml.cgb2 | Fitting the Compound Distribution based on the GB2 by the Method of Maximum Likelihood Estimation
ml.gb2 | Maximum Likelihood Estimation of the GB2 Based on the Full Log-likelihood
mlfit.gb2 | Fitting the GB2 by the Method of Maximum Likelihood Estimation and Comparison of the Fitted Indicators with the Empirical Indicators
MLfitGB2 | Fitting the GB2 by the Method of Maximum Likelihood Estimation and Comparison of the Fitted Indicators with the Empirical Indicators
MLfullGB2 | Maximum Likelihood Estimation of the GB2 Based on the Full Log-likelihood
mlh.gb2 | Maximum Likelihood Estimation of the GB2 Based on the Full Log-likelihood
MLprofGB2 | Maximum Likelihood Estimation of the GB2 Based on the Profile Log-likelihood
moment.cgb2 | Moments of the Compound Distribution based on the GB2
moment.gb2 | Moments and Other Properties of a GB2 Random Variable
Moments | Moments and Other Properties of a GB2 Random Variable

## -- N --

nlsfit.gb2 | Fitting the GB2 by Minimizing the Distance Between a Set of Empirical Indicators and Their GB2 Expressions
NonlinearFit | Fitting the GB2 by Minimizing the Distance Between a Set of Empirical Indicators and Their GB2 Expressions

## -- P --

pcgb2 | Compound Distribution based on the Generalized Beta Distribution of the Second Kind
pgb2 | The Generalized Beta Distribution of the Second Kind
pkl.cavgb2 | Fitting the Compound Distribution based on the GB2 by the Method of Pseudo Maximum Likelihood Estimation using Auxiliary Information
pl.cgb2 | Compound Distribution based on the Generalized Beta Distribution of the Second Kind
PlotsML | Cumulative Distribution Plot and Kernel Density Plot for the Fitted GB2
plotsML.gb2 | Cumulative Distribution Plot and Kernel Density Plot for the Fitted GB2
pofv.cgb2 | Fitting the Compound Distribution based on the GB2 by the Method of Maximum Likelihood Estimation
prcgb2 | Compound Distribution based on the Generalized Beta Distribution of the Second Kind
prof.gb2 | Profile Log-likelihood of the GB2 Distribution
proflogl.gb2 | Profile Log-likelihood of the GB2 Distribution
ProfLogLikelihood | Profile Log-likelihood of the GB2 Distribution
profml.gb2 | Maximum Likelihood Estimation of the GB2 Based on the Profile Log-likelihood
profscores.gb2 | Profile Log-likelihood of the GB2 Distribution

## -- Q --

qcgb2 | Quantiles and random generation of the Compound Distribution based on the GB2
qgb2 | The Generalized Beta Distribution of the Second Kind
qsr.cgb2 | Indicators of Poverty and Social Exclusion under the Compound Distribution based on the GB2
qsr.gb2 | Monetary Laeken Indicators under the GB2

## -- R --

rcgb2 | Quantiles and random generation of the Compound Distribution based on the GB2
rgb2 | The Generalized Beta Distribution of the Second Kind
rmpg.cgb2 | Indicators of Poverty and Social Exclusion under the Compound Distribution based on the GB2
rmpg.gb2 | Monetary Laeken Indicators under the GB2
RobustWeights | Robustification of the sampling weights
robwts | Robustification of the sampling weights

## -- S --

saveplot | Cumulative Distribution Plot and Kernel Density Plot for the Fitted GB2
scores.cavgb2 | Fitting the Compound Distribution based on the GB2 by the Method of Pseudo Maximum Likelihood Estimation using Auxiliary Information
scores.cgb2 | Fitting the Compound Distribution based on the GB2 by the Method of Maximum Likelihood Estimation
scoresh.gb2 | Full Log-likelihood of the GB2 Distribution
scoresp.gb2 | Full Log-likelihood of the GB2 Distribution
scoreU.cavgb2 | Variance Estimation under the Compound GB2 Distribution Using Auxiliary Information
scoreU.cgb2 | Variance Estimation of the Compound GB2 Distribution
scorez.cavgb2 | Variance Estimation under the Compound GB2 Distribution Using Auxiliary Information
sl.gb2 | Moments and Other Properties of a GB2 Random Variable

## -- T --

Thomae | Maximum Excess Representation of a Generalized Hypergeometric Function Using Thomae's Theorem

## -- U --

ULg | Maximum Excess Representation of a Generalized Hypergeometric Function Using Thomae's Theorem

## -- V --

Varest | Variance Estimation of the Parameters of the GB2 Distribution
varscore.cavgb2 | Variance Estimation under the Compound GB2 Distribution Using Auxiliary Information
varscore.cgb2 | Variance Estimation of the Compound GB2 Distribution
varscore.gb2 | Variance Estimation of the Parameters of the GB2 Distribution
veind.cavgb2 | Variance Estimation under the Compound GB2 Distribution Using Auxiliary Information
veind.cgb2 | Variance Estimation of the Compound GB2 Distribution
veind.gb2 | Variance Estimation of the Parameters of the GB2 Distribution
vepar.cavgb2 | Variance Estimation under the Compound GB2 Distribution Using Auxiliary Information
vepar.cgb2 | Variance Estimation of the Compound GB2 Distribution
vepar.gb2 | Variance Estimation of the Parameters of the GB2 Distribution
vl.gb2 | Moments and Other Properties of a GB2 Random Variable
vofp.cgb2 | Fitting the Compound Distribution based on the GB2 by the Method of Maximum Likelihood Estimation