Weibull-Weighted Lindley Distribution: Modelling of Heterogeneous Survival Patterns in COVID-19 Data
Keywords:
COVID-19 data, Hazard function, Frailty models, Lifetime distributions, Parameter estimation, Time-to-event data, Survival analysis, Weibull distribution, Weighted Lindley distributionAbstract
This paper introduces the Weibull-Weighted Lindley (WWL) distribution, a new three-parameter frailty-based model for time-to-event data characterized by unobserved heterogeneity. The WWL distribution arises by compounding the Weibull distribution (as the baseline survival model) with a Weighted Lindley distribution (as the frailty component), resulting in a highly flexible distribution that 6can accommodate increasing, decreasing, and hazard rates. We derive key properties of the model, including its probability density function, cumulative distribution function, survival function, and hazard function. Multiple estimation methods are explored. A comprehensive simulation study is conducted to evaluate the performance of these estimators. The model’s utility is demonstrated through its application to real-world COVID-19 survival datasets. In all cases, the WWL model provides an excellent fit compared to competing lifetime models, as measured by standard information criteria and goodness-of-fit tests. These findings highlight the WWL distribution as a powerful and adaptable tool for modeling complex survival data with latent heterogeneity.
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