GNU R 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.
