GB2: Generalized Beta Distribution of the Second Kind: properties, likelihood, estimation

GB2 is a simple package that 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. Formulae for various indicators of inequality and poverty under the GB2 are implemented. The GB2 is fitted using 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 vizualization and analysis of the results are provided. Variance estimation of the parameters is provided for the method of maximum pseudo-likelihood estimation. A compound distribution based on the GB2 is presented. This compound distribution can be calculated by a left or right tail decomposition. Density, cumulative distribution function, moments and quantiles for the compound distribution can be calculated. The compound distribution is fitted using the method of maximum likelihood estimation. The fit can be also adapted for the use of auxiliary information.