A Novel Inverse Statistical Model for Lifetime and Reliability Analysis

This paper introduces the Inverse Mustapha Type-II Distribution ($\text{IMU}{\hspace{0.17em}}_{II}D$), a novel lifetime model derived through the inverse transformation of the Mustapha Type-II distribution. Designed for modeling data on the positive real line, the $\text{IMU}{\hspace{0.17em}}_{II}D$ offers enhanced flexibility in reliability and survival analysis, particularly where traditional models fall short. We derive key statistical properties of the distribution, including moments, mean residual life, mean inactivity time, and entropy measures. Parameter estimation is explored using multiple methods, with simulation studies demonstrating the robustness of the estimators. The practical applications of the $\text{IMU}{\hspace{0.17em}}_{II}D$ are validated through applications to real-world datasets, where it outperforms competing lifetime models in goodness-of-fit tests. Our results highlight the $\text{IMU}{\hspace{0.17em}}_{II}D$ as a valuable tool for reliability analysis, survival studies, and related fields, providing a versatile alternative for practitioners.