An innovative data analysis method with theoretical foundation: Its pertinence in the realms of radiation and accounting

In real-world situations, a significant research focus is the development of innovative probabilistic techniques to accurately describe the phenomena being studied. These probabilistic techniques are efficiently employed to optimally depict real-world data in different practical fields. Acknowledging the important role of probabilistic techniques in practical situations, this paper introduces a new probability distribution. The proposed research focuses on applying the Lomax distribution and a cosine-oriented distributional technique to introduce a novel distribution termed the new cosine-trigonometric-Lomax (NCT-Lomax) distribution. Our analysis indicates that the NCT-Lomax distribution exhibits increased distributional flexibility, heavy-tailed characteristics, and optimal performance in modeling real-world data sets. We derive various mathematical characteristics of the NCT-Lomax distribution that are essential for understanding its behavior. Additionally, we explore various estimation techniques to obtain the estimators for the NCT-Lomax distribution. Furthermore, a simulation analysis was performed to assess the effectiveness of these techniques. To achieve benefits in practical situations, we utilize the NCT-Lomax distribution with two actual data sets from accounting and radiation-related domains. We showcase the practical benefits of the NCT-Lomax distribution compared to the Lomax distribution and its other variations by using three goodness-of-fit metrics and p-values. Our empirical analysis reveals that the NCT-Lomax distribution consistently surpassed the Lomax distribution and its various alternatives in offering the most suitable fit for the accounting and radiation data sets.