Abstract The use of probability distributions in engineering, environmental, actuarial, and biomedical sciences cannot be under-estimated. In recent years, the trigonometric distributions have gained significant attention due to their flexibility in modeling skewed and heavy-tailed data. This study proposes a new class of probability distributions embedding the trigonometric function within the Arctan generator, named as Arctan Uniform-G (ATU-G) family. The objective is to develop a new flexible model for skewed and heavy-tailed lifetime data, which is commonly encountered in reliability analysis. As a special case, the Arctan Uniform Fréchet (ATUF) distribution is discussed in detail by considering the Fréchet distribution as a baseline, keeping in view its importance as a statistical model in the area of both pure and applied sciences. Fundamental distributional characteristics of the proposed model, including reliability function, hazard rate function, and moments, are derived and discussed along with others. The parameters of the ATUF distribution are estimated using the maximum-likelihood method employing Monte Carlo simulation and a Bayesian framework with various loss functions. Bayesian posterior inference is carried out via the Metropolis–Hastings (MH) algorithm. Simulation results confirm the consistency and efficiency of the estimators. The empirical application demonstrates improved goodness-of-fit compared with existing Fréchet-type models. These findings highlight the ATUF distribution’s ability to model diverse hazard behaviors, indicating its broad utility in reliability and material research.
Huang et al. (Thu,) studied this question.
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