Generalized Beta Distribution of the Second Kind: Properties, Likelihood, Estimation
Comparison of the GB2, compound GB2 and kernel densities
Fitting the Compound Distribution based on the GB2 by the Method of Ma...
Compound Distribution based on the Generalized Beta Distribution of th...
Comparison of the compound GB2 and kernel densities by group
Fitting the Compound Distribution based on the GB2 by the Method of Ps...
Variance Estimation under the Compound GB2 Distribution Using Auxiliar...
Indicators of Poverty and Social Exclusion under the Compound Distribu...
Moments of the Compound Distribution based on the GB2
Quantiles and random generation of the Compound Distribution based on ...
Variance Estimation of the Compound GB2 Distribution
Sensitivity Analysis of Laeken Indicators on GB2 Parameters
Contour Plot of the Profile Log-likelihood of the GB2 Distribution
Parameters of the Fisk Distribution
The Generalized Beta Distribution of the Second Kind
Computation of the Gini Coefficient for the GB2 Distribution and its P...
Monetary Laeken Indicators under the GB2
Log Density of the GB2 Distribution
Full Log-likelihood of the GB2 Distribution
Fitting the GB2 by the Method of Maximum Likelihood Estimation and Com...
Maximum Likelihood Estimation of the GB2 Based on the Full Log-likelih...
Maximum Likelihood Estimation of the GB2 Based on the Profile Log-like...
Moments and Other Properties of a GB2 Random Variable
Fitting the GB2 by Minimizing the Distance Between a Set of Empirical ...
Cumulative Distribution Plot and Kernel Density Plot for the Fitted GB...
Profile Log-likelihood of the GB2 Distribution
Robustification of the sampling weights
Maximum Excess Representation of a Generalized Hypergeometric Function...
Variance Estimation of the Parameters of the GB2 Distribution
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.