Arcsine Ratio Sine Generalized Distributions with Applications to Biomedical and Engineering Data
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Abstract
Trigonometric distributions offer a powerful approach to solving complex problems in probability and statistical modeling. In this study, we introduce a novel class of distributions: the Arcsine Ratio Sine Generalized (ARS-G) family. We provide a complete set of explicit formulas for the family’s statistical properties. Our key illustration is the ARS-Weibull (ARS-W) distribution, which uses the Weibull model as its foundation. This particular model demonstrates remarkable flexibility, with its hazard function capable of assuming diverse shapes, including bump, bathtub, reversed bathtub, J-shaped, and L-shaped profiles. We thoroughly examine the ARSW distribution’s statistical properties and employ various established estimation methods to determine its parameters. Through rigorous Monte Carlo simulations, we confirm the consistency and stability of these estimation methods. We then showcase the ARS-W model’s practical value by applying it to three real-world lifetime datasets: guinea pig survival times, active repair times for a communication transceiver, and turbocharger failure times. The model not only provides robust parameter estimates and a strong goodness-of-fit for the right-skewed guinea pig and transceiver data, but also outperforms traditional distributions (Weibull, Gumbel, Gamma, and Lognormal) for the left-skewed turbocharger dataset
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