The modified Muth distribution: Statistical properties, entropy measures, and parameter estimation

In this study, the modified Muth distribution was introduced as a parsimonious lifetime model obtained by structurally modifying the Muth survival function. The proposed construction preserves the scale-family property while altering tail behavior and cumulative hazard growth. A statistical analysis was presented, including derivations of moments, the moment-generating function, and several entropy measures. Parameter estimation was carried out using maximum likelihood, and interval estimation was performed via the Fisher information matrix. The performance of the model was examined through extensive simulation studies and a real-world data application involving strength measurements of carbon fibers. In this application, the modified Muth distribution provides a competitive and, in several cases, improved fit compared with commonly used lifetime models.