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Introduction In survival analysis, various lifetime distributions are used to model hazard and survival functions. This study introduces a modified Weibull distribution capable of exhibiting increasing, decreasing, constant, and bathtub-shaped hazard rates. The distribution's flexibility allows it to better capture different density patterns like bimodal observed in real-world data, especially in medical settings. Methodology The proposed distribution's properties, including its hazard and survival functions, are explored in detail. Data from hospital records was used to validate the model. Parameters are estimated via the expectation-maximization (EM) algorithm, with standard errors and confidence intervals calculated. A comparison is drawn with other modified Weibull models to assess the performance. Results The model demonstrates a good fit for the hospital dataset, providing a robust estimation of survival probabilities across different time periods. The EM algorithm ensures precise parameter estimation, and the results show the model's capability to capture varying hazard patterns effectively. Kaplan-Meier survival curves are plotted and compared with the survival curve from the proposed model, showing strong alignment. Conclusion The modified Weibull distribution introduced in this study offers a versatile tool for modeling different hazard rate patterns. The model's strong performance, validated through real hospital data, suggests it could be a valuable addition to survival analysis, outperforming other modified Weibull models in terms of fit and flexibility.
Rangoli et al. (Sun,) studied this question.