A New Family of Weighted T-X Distributions with Environmental Health and Textile Engineering Applications
Résumé
This study presents a novel framework for modeling fine particulate matter (PM2.5) hazards and the tensile strength of polyester, using a newly formulated family of weighted T-X distributions, termed the Odd Reparametrized Exponential Transformed-X (ORET-X) family. With growing concerns over the health and environmental risks associated with PM2.5 exposure—particularly its link to respiratory and cardiovascular diseases—and the reliability challenges posed by polyester tensile strength, this work aims to offer a more flexible modeling approach for both fields. The ORET-X family builds upon the exponential distribution via reparametrization, introducing an odd function transformation to enhance the modeling of hazard functions and tail behavior. Specifically, the Odd Reparametrized Exponential Transformed-Lomax (ORET-L) distribution, a subclass of the ORET-X family, was developed and analyzed. The study utilized both Bayesian and non-Bayesian estimation methods, with results demonstrating improved model accuracy as sample sizes increased. Bayesian estimation showed reduced bias and lower Root Mean Squared Error (RMSE) across parameters, particularly at smaller sample sizes, underscoring the robustness of the parameter estimates. The ORET-X family offers significant promise in environmental health, engineering, and other domains requiring flexible hazard-based distributions. Our results suggest that the ORET-L model provides superior fit and predictive accuracy for modeling PM2.5 exposure mortality, as shown through various statistical performance metrics and visual assessments, making it a compelling tool for both environmental risk modeling and engineering applications.
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