# 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

## 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