A Maxwell‐Generated Distribution Based on Logistic Growth Dynamics for Lifetime Data Modeling

This paper introduces a new lifetime distribution, called the Maxwell–logistic growth lifetime (MLGL) distribution, obtained by incorporating a logistic‐growth hazard structure into the Maxwell‐generated family of distributions. In contrast to Maxwell‐generated models based on conventional baseline lifetime distributions, the MLGL model incorporates a baseline hazard governed by a logistic‐growth ordinary differential equation, providing an interpretable mechanism for dynamically evolving failure risk. The resulting model admits an identifiable three‐parameter representation and allows the underlying hazard dynamics to vary according to the logistic‐growth parameters. Several distributional and reliability properties are derived. A Monte Carlo simulation study is conducted to examine the finite‐sample performance of the estimators. Applications to real lifetime datasets demonstrate that the proposed model provides competitive fits relative to several classical and recently proposed lifetime distributions.