Comparison of Estimation Methods for the Contaminated Weibull Distribution and Applications to Medical Data

Authors

Yusuf Olatunji Bello, "Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Kingdom of Saudi Arabia AND Institute for Advanced Medical Research and Training, College of Medicine, University of Ibadan, Oyo State, Nigeria
Farouq Mohammad A. Alam, Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Kingdom of Saudi Arabia
Abdulkader Monir Daghistani, Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Kingdom of Saudi Arabia

Abstract

The Contaminated Weibull (CWB) distribution was introduced as a robust alternative for modeling lifetime and survival data, particularly in scenarios involving outliers or contamination within the dataset. The CWB distribution accounted for a mixture of a reference Weibull distribution and contaminated observations. An extensive Monte Carlo simulation was conducted to assess the performance of various parameter estimation methods for the CWB distribution. Seven estimation methods were compared: Maximum Likelihood Estimation (MLE), Least Squares Estimation, Weighted Least Squares Estimation, Maximum Product Spacing Estimation, Cramér-von Mises Estimation, Anderson-Darling Estimation, and Robust Anderson-Darling Estimation. The results showed that MLE outperformed other methods in terms of bias and Root Mean Squared Error (RMSE), particularly as sample size increases. The CWB distribution was applied to two real-world medical datasets: the time to infection of kidney dialysis patients and the survival time of patients undergoing chemotherapy treatment. In both cases, the CWB distribution provides better fit than the conventional Weibull distribution. These findings highlight the potential of the CWB distribution in medical and survival data analysis, particularly in the presence of contamination. The CWB distribution offers a versatile and effective tool for modeling positively skewed data with contamination, providing more reliable estimates in the presence of outliers compared to traditional models.

First Page

25

Last Page

51

Recommended Citation

Bello, Yusuf Olatunji; Alam, Farouq Mohammad A.; and Daghistani, Abdulkader Monir (2026) "Comparison of Estimation Methods for the Contaminated Weibull Distribution and Applications to Medical Data," The Journal of King Abdulaziz University: Science: Vol. 36: Iss. 1, Article 3.
DOI: https://doi.org/10.64064/1658-4252.1014

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This work is licensed under a Creative Commons Attribution 4.0 International License.