A novel Arctan-based model: Bayesian analysis, progressive censoring, and practical applications

For modeling and analyzing complex datasets in various scientific fields, probability distributions are crucial. Nevertheless, complex characteristics found in real-world data, like skewness, heavy tails, or high variability, are frequently missed by classical distributions. This study suggests a novel extension of the power hazard model based on the arctan-X family, the arctan power hazard (AT-PH) distribution, to overcome these drawbacks. The AT-PH distribution is constructed by integrating the baseline power hazard distribution with the arctan-X family framework. The suggested model improves the classical power hazard distribution's adaptability without adding parameters and makes it more capable of handling a range of data behaviors. To lay the theoretical groundwork for the model, several important characteristics were determined, such as moments, incomplete moments, the mean residual and reversed residual life, and entropy measures. Using progressively censored data, we obtain Bayesian and maximum likelihood estimates for the AT-PH distribution parameters as well as important reliability metrics like the hazard rate and reliability functions. Through the use of the Metropolis–Hastings algorithm, Bayesian analysis is carried out with independent gamma priors under asymmetric and symmetric loss functions. Asymptotic confidence intervals and Bayesian credible intervals are investigated. Monte Carlo simulations, under progressive censoring schemes, show that the suggested techniques are high numerical stability and exceptional computational accuracy. The practical usefulness of the proposed model is shown through two real-world datasets relating to engineering (fiber strength in glass) and hydrogeology (maximum flood level). From the statistical analysis, the AT-PH model surpasses the other competing models due to lower values of information criteria and greater values of the Kolmogorov–Smirnov test p-value (0.972 for the first data set and 0.4572 for the second data set). Performance comparisons show the promise of the flexibility of the proposed model in handling complicated failure cases.