Breaking the norm : approaches for symmetric, positive, and skewed data

Abstract

This research contributes to the advancement of flexible and interpretable models within distribution theory, which is a fundamental aspect of numerous academic disciplines. This study investigates and presents the derivative-kernel approach for extending distributions. This method yields new distributions for symmetric, skew, and positive data, making it applicable for a wide range of modelling tasks. These newly derived distributions enhance the normal and gamma distributions by incorporating easily interpretable and identifiable parameters while retaining tractable mathematical properties. Furthermore, these models have a solid statistical foundation for simulation and prediction through stochastic representations. Additionally, these models demonstrate proficient flexibility and modelling performance when applied to real data. The introduced skew distribution presents a new skewing mechanism that combines the best features of current leading methods. Consequently, this leads to improved accuracy and flexibility when modelling skewed data patterns. In today's rapidly evolving data landscape, with increasingly intricate data structures, these advancements provide vital tools for effectively interpreting and analysing diverse data patterns encountered in economics, psychology, engineering, and biology.