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.