On Properties of a New Generalization of the Log-Logistic Distribution and Its Application

Recent developments in distribution theory emphasize the problems researchers face and propose different models so that lifetime datasets can be better evaluated and studied in various application domains.In other words, there is a need to introduce applicable models to better study natural phenomena.An essential goal for proposing, extending, or generalizing (models or their classes) is to explain how life expectancy occurs in physics, computer science, insurance, health care, medicine, engineering, biology, industry, communications, etc.The well-known and basic distributions, such as the log-logistic, exponential, Rayleigh, Weibull, and Gamma distributions, are very limited in their properties and need more flexibility.Log-logistic distribution plays a significant role in various fields due to its flexibility in modeling lifetime data and its ability to account for diverse real-world phenomena.Its widespread applications span reliability analysis, survival studies, and economic modeling, demonstrating its importance in theoretical and practical contexts.However, despite its utility, the standard log-logistic distribution lacks the adaptability required to address more complex datasets or emerging challenges in modern applications.This underscores the necessity of proposing generalized versions that extend its capabilities.In this work, we introduce a novel extension of the log-logistic distribution that enhances its flexibility, allowing for more accurate and practical applications across various domains.