A unified parsimonious exponential-G family for modeling real-world data: theory and statistical inference

This paper introduces a new parsimonious class of statistical models, called the flexible exponential-G (FEx-G) family. The primary motivation for proposing the FEx-G family lies in its structural simplicity and adaptability, as it accommodates any baseline distribution without introducing additional shape parameters, thereby avoiding unnecessary model complexity. Unlike many existing generator-based families, the FEx-G family is independent of previously established generators, making it a distinct and original contribution to distribution theory. Despite its parsimonious structure, the FEx-G family exhibits remarkable flexibility, being capable of modeling both monotone and nonmonotone failure rate functions, and therefore is suitable for analyzing a wide range of non-negative real-world data. A special case, termed the flexible exponential-Kumaraswamy (FExKw) distribution, is investigated in detail. The parameters of the FExKw model are estimated using nine different estimation methods, and extensive simulation studies are conducted to evaluate and rank their performance. The practical usefulness of the FExKw distribution is illustrated through applications to four real-life datasets from environmental science, industry, and medicine, where it demonstrates superior performance compared with several well-established competing distributions.