A Survival Weighted Resilience Framework for the Marshall–Olkin Distribution with Applications in Environmental and Biomedical Modeling
Year: 2026
Type: article
Abstract: This paper develops a survival weighted hazard interpretation of the Marshall--Olkin extension for lifetime distributions. The resulting formulation, termed the Resilience Distribution (RD), introduces a parameter θ>0 that modulates the baseline hazard through the survival probability, providing a representation of resilience and hazard damping in reliability systems. The framework allows flexible hazard patterns, including increasing, decreasing, and non-monotonic shapes. Key statistical properties, including the density, survival and hazard functions, quantile function, moments, and order statistics, are derived. Theoretical results on stochastic ordering, tail behavior, and hazard elasticity are established. Parameter estimation is performed using maximum likelihood, supported by a simulation study. A special case based on the Lindley distribution is applied to real datasets, demonstrating the flexibility and interpretability of the proposed framework for modeling lifetime data.
DOI: 10.66721/wwezw471
Authors: Shameera T, Bindu P.P.
Institution: MES Mampad College (Autonomous)
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7214087389