Inference for a Hidden Truncated (Both-Sided) Bivariate Pareto (II) Distribution

Abstract

The Pareto distribution is a simple model for non negative data with a power law probability tail. Income and wealth data are typically modeled using some variant of the classical Pareto distribution. In practice, it is frequently likely that the observed data have been truncated with respect to some unobserved covariable. In this paper, a hidden truncation formulation of this scenario is proposed and analyzed. A bivariate Pareto (II) distribution is assumed for the variable of interest and the unobserved covariable. Distributional properties of the resulting model are investigated. A variety of parameter estimation strategies (under the classical set up) are investigated.

Keywords:

• Bivariate Pareto (II) distribution
• Fractional method of moments
• Hidden truncation
• Limiting behavior of the hidden truncated Pareto (II) distribution
• Quantile method of estimation

Mathematics Subject Classification:

• 62E
• 62F