Graphical representations and associated goodness-of-fit tests for Pareto and log-normal distributions based on inequality curves

Abstract

The Pareto and the Log-normal distributions can be characterised by having constant inequality curves. After providing formal proofs, these results will be exploited to obtain graphical and analytical tools for analysis and goodness-of-fit tests for these distributions. Order-statistics-based estimators of the curves will be presented and discussed. Examples with simulated and real-data will be used to show how the tools presented work in practice.

Keywords:

• Tail index
• Pareto tail
• graphical analysis
• nonparametric estimation
• parametric bootstrap

Acknowledgments

The authors would like to thank two anonymous referees whose constructive comments lead to an improved version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).