Two New Entropy Estimators for Testing Exponentiality with Type-II Censored Data

TL;DR

This paper introduces two new entropy estimators for Type-II censored data and demonstrates their improved bias, RMSE, and test power over existing methods through simulation studies.

Contribution

The paper presents two novel entropy estimators for Type-II censored data and develops new goodness-of-fit tests with superior performance.

Findings

Second estimator has less bias and RMSE than leading estimator.

New test statistics outperform existing ones in power against specific alternatives.

Simulation confirms improved accuracy and effectiveness of proposed methods.

Abstract

This paper proposes two estimators of the joint entropy of the Type-II censored data. Consistency of both estimators is proved. Simulation results show that the second one shows less bias and root of mean square error (RMSE) than leading estimator. Also, two goodness of fit test statistics based on the Kullback-Leibler information with the Type-II censored data are established and their performances with the leading test statistics are compared. We provide a Monte Carlo simulation study which shows that the test statistics $T^{(1)}_{m,n,r}$ and $T^{(2)}_{m,n,r}$ show better powers than leading test statistics against the alternatives with monotone decreasing and monotone increasing hazard functions, respectively.