The Kavya-Manoharan Lomax distribution with application to renewable rnergy systems

This paper introduces the Kavya-Manoharan Lomax (KM-Lomax) distribution, a novel heavy-tailed model developed by applying the KM-G transformation to the classical Lomax distribution. The KM-Lomax model provides enhanced flexibility in its density and hazard functions, making it capable of capturing a wide range of data behaviours, including right-skewed and reversed J-shaped patterns. Key statistical properties are derived, including moments, moment-generating functions, incomplete and conditional moments, and entropy measures such as Shannon, Rényi, Tsallis, and Arimoto. Estimation is addressed through the maximum likelihood method, with its performance evaluated via Monte Carlo simulation. The model's practical utility is demonstrated through applications to real-world data, with particular emphasis on renewable energy systems, where it effectively models extreme variability and supports reliability analysis and risk quantification. Comparative analysis confirms the KM-Lomax distribution's superior fit relative to several existing models, establishing its value as a flexible and robust tool for complex data modelling.