Arctan Power Half-Logistic Model: A Bayesian Approach to Progressively Censored Engineering Data

Abstract

The motivation behind the creation of new statistical models is primarily driven by the need to accurately describe complex data and related phenomena. This article introduces the arctan power half logistic distribution, a new and more flexible extension of the power half logistic distribution. The proposed model’s hazard rate function is highly versatile, capable of displaying decreasing, J-shaped, or reversed J-shaped patterns. We derive its key statistical properties and investigate its application to progressively Type-II censored data. Parameter estimation is conducted using both maximum likelihood and Bayesian frameworks, the latter incorporating informative and non-informative priors across multiple loss functions. Given the analytical intractability of the posterior distributions, we employ Markov Chain Monte Carlo techniques for numerical approximation. Monte Carlo simulations demonstrate that Bayesian point and interval estimates generally outperform frequentist approaches, maintaining coverage probabilities near 95%. Finally, the model’s superiority is validated using a real-world engineering dataset, where it consistently outperforms several established competing distributions.OPEN ACCESS Received: 21/02/2026 Accepted: 20/04/2026

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