Analyzing Real Data by a New Heavy-Tailed Statistical Model

Abstract

This study presents the power Mira distribution, an innovative three-parameter probability model that improves baseline distributions by including an extra shaping parameter. The suggested distribution has exceptional adaptability in representing various data characteristics, such as left and right skewness, declining trends, and unimodal patterns. These characteristics render it exceptionally appropriate for modeling risk-related data, an essential component of actuarial science and insurance analytics. We do an extensive theoretical study, delineating essential statistical features and offering a robust framework for parameter estimation. Critical risk metrics, including value-at-risk and tail value-at-risk, are calculated and assessed using comprehensive numerical simulations, validating the precision and efficacy of the suggested estimators. We illustrate the practical value of the power Mira distribution by applying it to a real-world insurance loss dataset and comparing its performance with established models. The findings underscore its exceptional goodness-of-fit and flexibility, affirming its capability as an effective instrument for risk assessment and financial modeling.