Characterizations of a family of bivariate Pareto distributions

Abstract

In the present paper, we study properties of a family of bivariate Pareto distributions. The well known dullness property of the univariate Pareto model is extended to the bivariate setup. Two measures of income inequality viz. income gap ratio and mean left proportional residual income are defined in the bivariate case. We also introduce bivariate generalized failure rate useful in reliability analysis. Characterizations, using the above concepts, for various members of the family of bivariate Pareto distributions are derived.

Keywords

• Bivariate Pareto distributions
• characterization
• dullness property
• income gap ratio
• generalized failure rate