# Assessing uncertainty: A study of entropy measures for Burr XII distribution under progressive Type-II censoring

## TL;DR

This paper evaluates different entropy measures for the Burr XII distribution under a specific type of data censoring and finds some measures perform better in simulations and cancer data analysis.

## Contribution

The study introduces and evaluates five entropy measures under progressive Type-II censoring for the Burr XII distribution.

## Key findings

- Maximum likelihood estimators for entropy measures show low bias and variance across different censoring schemes.
- Rényi and Havrda-Charvát entropy measures performed most robustly in simulations and real data analysis.
- Application to breast cancer data shows practical utility in distinguishing benign and malignant cases.

## Abstract

This research study focuses on calculating five entropy measures (Shannon, Rényi, Havrda-Charvát, Arimoto, and Tsallis) for the Burr XII distribution, utilizing progressive Type-II censoring. The study derives maximum likelihood estimators for each entropy measure and constructs two-sided confidence intervals. A comprehensive simulation study evaluates the performance of these estimators across various sample sizes and parameter settings. The results demonstrate that the proposed methods achieve low bias and variance under different censoring schemes, with coverage probabilities consistently close to the nominal level. Additionally, an application to the Wisconsin Breast Cancer Database highlights the practical utility of the entropy estimators in distinguishing between benign and malignant cases. Among the measures evaluated, the Rényi, Havrda-Charvát entropy measures exhibited the most robust performance in both simulation and real life data analysis.