A computational method for estimating Burr XII parameters with complete and multiple censored data

TL;DR

This paper develops a new computational approach using the Cross-Entropy method combined with Maximum Likelihood Estimation to accurately estimate Burr XII distribution parameters for both complete and censored data, enhancing applications in risk and lifetime analysis.

Contribution

It introduces a novel CE-based MLE method for Burr XII parameters applicable to censored and complete data, improving estimation accuracy over existing methods.

Findings

The proposed method performs well across various sample sizes and parameter settings.

It outperforms traditional estimation techniques in censored data scenarios.

Simulation results demonstrate improved accuracy and robustness.

Abstract

Flexibility in shape and scale of Burr XII distribution can make close approximation of numerous well-known probability density functions. Due to these capabilities, the usages of Burr XII distribution are applied in risk analysis, lifetime data analysis and process capability estimation. In this paper the Cross-Entropy (CE) method is further developed in terms of Maximum Likelihood Estimation (MLE) to estimate the parameters of Burr XII distribution for the complete data or in the presence of multiple censoring. A simulation study is conducted to evaluate the performance of the MLE by means of CE method for different parameter settings and sample sizes. The results are compared to other existing methods in both uncensored and censored situations.