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

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.