A Survival Weighted Resilience Framework for the Marshall–Olkin Distribution with Applications in Environmental and Biomedical Modeling
- 1Department of Statistics, MES Mampad College, Malappuram, Kerala, India
- 2Department of Statistics, Govt. Arts & Science College, Kozhikode, Kerala, India
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.
Related
- Subdivision-based collocation methods for time fractional convection diffusion reaction equation with environmental and biomedical applications
- Functional and Object-Oriented Data Analysis for Complex Biomedical, Environmental and Socioeconomic Systems
- Beyond an Ethos or Inflexible Checklist of Research Practices: Grounding Open Science in a Biomedical Research Ethics Framework
- Statistical inference and applications of Kumaraswamy Odd Perks power Lomax distribution
- The Cauchy–Modified Garima Distribution: Applications to Device Lifetimes and Aircraft Windshield Failures
BibTeX
@article{shameera2026survival,
title = {{A Survival Weighted Resilience Framework for the Marshall–Olkin Distribution with Applications in Environmental and Biomedical Modeling}},
author = {Shameera T and Bindu P.P.},
journal = {Reliability: Theory \& Applications},
year = {2026},
month = sep,
doi = {10.66721/wwezw471},
url = {https://doi.org/10.66721/wwezw471},
note = {CC BY-NC},
}
RIS
TY - JOUR
TI - A Survival Weighted Resilience Framework for the Marshall–Olkin Distribution with Applications in Environmental and Biomedical Modeling
AU - Shameera T
AU - Bindu P.P.
PY - 2026
DA - 2026/09/01
JO - Reliability: Theory & Applications
DO - 10.66721/wwezw471
UR - https://doi.org/10.66721/wwezw471
AB - 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.
SN - 1932-2321
ER -