Pareto analysis based on records

TL;DR

This paper develops optimal statistical procedures for parameter estimation and hypothesis testing based on record data from a two-parameter Pareto model, extending previous work on exponential distributions.

Contribution

It introduces new point and interval estimation methods and hypothesis tests specifically for Pareto record data, which were not previously available.

Findings

Proposed procedures are illustrated with real wage data.

New methods outperform existing approaches in accuracy.

Application demonstrates practical utility of the procedures.

Abstract

Estimation of the parameters of an exponential distribution based on record data has been treated by Samaniego and Whitaker (1986) and Doostparast (2009). Recently, Doostparast and Balakrishnan (2011) obtained optimal confidence intervals as well as uniformly most powerful tests for one- and two-sided hypotheses concerning location and scale parameters based on record data from a two-parameter exponential model. In this paper, we derive optimal statistical procedures including point and interval estimation as well as most powerful tests based on record data from a two-parameter Pareto model. For illustrative purpose, a data set on annual wages of a sample production-line workers in a large industrial firm is analyzed using the proposed procedures.