The exponentiated Ailamujia distribution: Properties and application

This paper introduces the exponentiated Ailamujia distribution (EAD), extending the Ailamujia distribution (AD) to offer greater versatility in modeling positively skewed data. The core contribution lies in the rigorous derivation and examination of EAD's reliability functions, including failure rate, survival, and mean waiting time functions, among others. Our analysis reveals novel algebraic expressions that deepen the understanding of these functions' behavior under varying conditions. Key findings include the identification of the increasing failure rate and mean waiting time (MWT) functions, contrasted by the decreasing mean residual life (MRL) function. We provide a thorough parameter estimation framework for EAD within both classical and Bayesian contexts, introducing innovative comparisons across different estimators. Through a Monte Carlo simulation study, we establish the superior accuracy of Bayesian estimators (BEs) over Maximum Likelihood Estimators (MLEs) and Generalized Maximum Likelihood Estimators (GMLEs). These results are not only theoretically significant but also practically impactful, as evidenced by the application of EAD to real-world data, particularly active repair times for an airborne communication transceiver, where EAD outperforms other one- and two-parameter existing models.