The development and implementation of odd-exponential-ailamujia distribution in python: properties and application in...

This study introduces the Odd-Exponential-Ailamujia (OEA) distribution, a novel extension of the Ailamujia distribution via the T-X family, offering enhanced flexibility for modeling complex lifetime data in reliability and survival analysis. Key statistical properties, including moments, moment-generating function, characteristic function, mean residual life, and mean waiting time, are derived using binomial and Taylor series expansions, transforming intractable integrals into computable forms and enabling precise approximation of distributional behavior. The hazard rate function exhibits diverse shapes (increasing, decreasing, or unimodal), controlled by parameters, making the proposed model adaptable to varied failure patterns. Applied to aircraft windshield failure data, the OEA distribution demonstrates superior fit over competing models through goodness-of-fit tests, various plots of reliability measures, 3D surface interactions, and heatmaps revealing parameter-driven correlations. Efficient Python implementation to ensures scalable inference. The OEA distribution emerges as a robust, versatile tool for reliability engineering, survival modeling, and probabilistic forecasting, effectively capturing real-world failure dynamics.