Testing Exponentiality Based on R\'enyi Entropy With Progressively Type-II Censored Data

TL;DR

This paper develops a new goodness of fit test for exponentiality using Re9nyi entropy with progressively Type-II censored data, demonstrating superior power over existing tests through simulation.

Contribution

It introduces a novel test statistic based on Re9nyi Kullback-Leibler information for censored data, with a simple entropy estimator and improved performance.

Findings

Proposed test outperforms existing tests in power.

New entropy estimator for censored data.

Effective for various hazard function shapes.

Abstract

We express the joint R\'enyi entropy of progressively censored order statistics in terms of an incomplete integral of the hazard function, and provide a simple estimate of the joint R\'enyi entropy of progressively Type-II censored data. Then we establish a goodness of fit test statistic based on the R\'enyi Kullback-Leibler information with the progressively Type-II censored data, and compare its performance with the leading test statistic. A Monte Carlo simulation study shows that the proposed test statistic shows better powers than the leading test statistic against the alternatives with monotone increasing, monotone decreasing and nonmonotone hazard functions.