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.

Author
Monique Graf <monique.p.n.graf@bluewin.ch>, Desislava Nedyalkova <desislava.nedyalkova@gmail.com>.
Date of publication
2015-05-11 23:48:49
Maintainer
Desislava Nedyalkova <desislava.nedyalkova@gmail.com>
License
GPL (>= 2)
Version
2.1

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

Files in this package

GB2
GB2/NAMESPACE
GB2/R
GB2/R/Varest.R
GB2/R/MLfitGB2.R
GB2/R/Indicators.R
GB2/R/CompoundAuxVarest.r
GB2/R/ProfLogLikelihood.R
GB2/R/Fisk.R
GB2/R/Thomae.R
GB2/R/Contindic.R
GB2/R/CompoundMoments.R
GB2/R/Gini.R
GB2/R/MLprofGB2.R
GB2/R/MLfullGB2.R
GB2/R/LogLikelihood.R
GB2/R/CompoundAuxDensPlot.r
GB2/R/GB2.R
GB2/R/CompoundVarest.R
GB2/R/PlotsML.R
GB2/R/CompoundQuantiles.R
GB2/R/CompoundFit.R
GB2/R/NonlinearFit.R
GB2/R/Moments.R
GB2/R/RobustWeights.R
GB2/R/Contprof.R
GB2/R/CompoundDensPlot.r
GB2/R/CompoundIndicators.R
GB2/R/Compound.R
GB2/R/CompoundAuxFit.R
GB2/R/LogDensity.R
GB2/MD5
GB2/DESCRIPTION
GB2/man
GB2/man/CompoundVarest.Rd
GB2/man/RobustWeights.Rd
GB2/man/CompoundMoments.Rd
GB2/man/ProfLogLikelihood.Rd
GB2/man/Fisk.Rd
GB2/man/MLprofGB2.Rd
GB2/man/Indicators.Rd
GB2/man/Moments.Rd
GB2/man/Contprof.Rd
GB2/man/CompoundIndicators.Rd
GB2/man/MLfullGB2.Rd
GB2/man/CompoundDensPlot.Rd
GB2/man/PlotsML.Rd
GB2/man/LogLikelihood.Rd
GB2/man/MLfitGB2.Rd
GB2/man/Thomae.Rd
GB2/man/CompoundFit.Rd
GB2/man/Contindic.Rd
GB2/man/gb2.Rd
GB2/man/Varest.Rd
GB2/man/CompoundAuxFit.Rd
GB2/man/NonlinearFit.Rd
GB2/man/Gini.Rd
GB2/man/CompoundAuxVarest.Rd
GB2/man/CompoundAuxDensPlot.Rd
GB2/man/Compound.Rd
GB2/man/LogDensity.Rd
GB2/man/CompoundQuantiles.Rd