A Survival Weighted Resilience Framework for the Marshall–Olkin Distribution with Applications in Environmental and Biomedical Modeling

Shameera T; Bindu P.P.

doi:10.66721/wwezw471

Authors

Shameera T Department of Statistics, MES Mampad College, Malappuram, Kerala, India Author
Bindu P.P. Department of Statistics, Govt. Arts & Science College, Kozhikode, Kerala, India Author

DOI:

https://doi.org/10.66721/wwezw471

Keywords:

Resilience modeling, Marshall–Olkin extension, Hazard rate function, Lindley distribution

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.

Author Biography

Bindu P.P., Department of Statistics, Govt. Arts & Science College, Kozhikode, Kerala, India

Dr. Bindu P. P. is an Associate Professor of Statistics at Government Arts and Science College, Kozhikode, Kerala, India. Her research interests include distribution theory, reliability analysis, survival modeling, statistical inference, and applied probability. She has published extensively in national and international journals and is actively engaged in postgraduate and doctoral research supervision.

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