Estimating flexible Weibull extension models under progressive Type-II censoring presents a statistical challenge due to the truncation of data at varying time points. This study proposes a parametric approach to estimate these models, accommodating the unique censoring mechanism. The flexible Weibull extension allows for a versatile representation of survival data, incorporating shape parameters that adapt to different hazard functions. Methodologically, maximum likelihood estimation is employed, leveraging the observed data and the censoring information effectively. The study explores the theoretical foundations and practical implications of this estimation technique, highlighting its applicability in analysing survival times subject to progressive Type-II censoring. Simulation studies are conducted to assess the performance of the proposed method under various scenarios, demonstrating its robustness and accuracy. Finally, real-world data examples illustrate the utility of the approach in modeling and interpreting survival data affected by progressive Type-II censoring, thereby contributing to advancements in statistical survival analysis methodologies.

Flexible Weibull extension models, Progressive Type-II censoring, Parametric estimation

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