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

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.