Odd-Fréchet Log-Logistic Distribution with Statistical Properties and Applications

Abstract

This manuscript introduces the Odd Fréchet Log-Logistic (OFrLL) distribution as a new extension of the Log-Logistic distribution within the Odd Fréchet G family. The proposed distribution’s key functions, including the probability density function, cumulative distribution function and hazard function are presented along with graphical representations. We derive essential mathematical properties, reliability characteristics, generating functions and entropy measures for the OFrLL distribution. Parameter estimations are conducted using various classical estimation approaches, with a comprehensive simulation study assessing their performance. The practical applicability of the OFrLL distribution is demonstrated through real-world data on foreign direct investment in India and CO₂ emissions, validating the model’s effectiveness.