Statistical Analysis of the Induced Ailamujia Lifetime Distribution with Engineering and Bidomedical Applications

Accurate modeling of industrial and biomedical data is often challenging due to skewness, heavy tails, and complex variability, which traditional probability distributions fail to capture. To address this, we propose the Induced Ailamujia Lifetime Distribution (IALD), a flexible generalization of the Ailamujia distribution developed via an induced transformation. The IALD accommodates diverse dataset characteristics through a wide range of probability density and hazard rate shapes. Several key statistical properties are derived, including moments, reliability measures, quantile and generating functions, probability weighted moments, and entropy measures. Model parameters are estimated using six classical methods, with their performance assessed through simulation. The practical utility of the IALD is demonstrated using two real datasets from biomedical and industrial fields, where it consistently outperforms existing lifetime models. These results confirm the IALD as a powerful and promising tool for reliability, engineering, and biomedical data analysis.