Abstract

Many lifetime analysis, such as engineering, biology, survival, actuarial and medical sciences, heavily rely on the two-parameter compound Rayleigh exponential distribution, which is well-known in statistical theory. Because of their ability to successfully handle small sample sizes and involve prior knowledge, Bayesian techniques are crucial for estimating the parameters of the compound Rayleigh exponential distribution. This study presents the estimation of the compound Rayleigh exponential distribution unknown parameters using Bayesian and non-Bayesian estimation techniques, including maximum likelihood estimation, maximum product spacing, least square estimator, weighted least square estimator, Cramer-Von-Mise estimator, Anderson-Darling estimator, and Bayesian techniques with informative and non-informative priors based on different loss functions. Additionally, we used several methods to obtain the confidence intervals for the unknown parameters, such as the approximate and Bootstrap methods. The effectiveness of these estimators is evaluated through a Monte Carlo simulation study. Furthermore, we are committed to investigating three widely recognized risk metrics: the value at risk, the tail value at risk, and the tail variance premium. These findings are helpful for actuarial risk researchers who depend on risk measurement fitting when evaluating Bayesian tools for effectively modeling actuarial sciences. Finally, different applications taken from several areas are examined to illustrate the practical usefulness of the compound Rayleigh exponential distribution. Using various model selection criteria, the introduced model is contrasted with that of several well-known distributions. Our empirical findings indicate that the suggested model has superior goodness-of-fit to the other models examined.

Abstract

A well-developed road network provides good services for road consumers. Most roads in the world are paved with flexible materials. Bitumen has viscous-elastic properties and is very sensitive to temperature. It plays a vital role in producing hot mix asphalt and influences the performance of HMA pavement. Flexible pavements are associated with extreme temperatures, which can cause rutting and fatigue cracking. Pavement distress shortens service life and increases maintenance costs. This research focused on improving pavement resistance to distress by modifying bitumen's conventional properties with alternative materials, such as shredded PET plastic. In this study, two stages were applied. The first stage was collecting samples, and the second stage determined the conventional properties of bitumen by adding 3%, 6%, and 9% of shredded PET plastic to the bitumen. Penetration, ductility, and softening point tests were performed to analyze the conventional behavior of bitumen. Finally, top-down and bottom-up cracks are used to evaluate rutting damage, with 3D-Move analysis software that accounts for moving vehicles under various loads and speeds. From the conventional bitumen test, adding 3% PET plastic to the bitumen has no significant effect on penetration grade, Ductility, or softening point. However, when 6% and 9% PET by weight of bitumen mixed, the penetration grade, ductility, and softening result become 49.3mm, 45.5mm, 97mm, 85mm, and 57mm and 62oC, respectively compared with the penetration grade, ductility, and softening point value of unmodified bitumen (66.5mm, 142cm, and 48.9oC). Besides, the 3D-Move Analysis software results show that asphalt binders with higher PET plastic content best resist rutting, top-down cracking, and bottom cracks.