A New Right-Skewed One-Parameter Distribution with Mathematical Characterizations, Distributional Validation, and Actuarial Risk Analysis, with Applications

Abstract

Skewed probability distributions are important when modeling skewed data sets because they provide a way to describe the shape of the distribution and estimate the likelihood of extreme events. Asymmetric probability distributions have the potential to handle and assess problems in actuarial risk assessment and analysis. To that end, we present a new right-skewed one-parameter distribution. In this work and for this purpose, a right-skewed probability distribution was derived and analyzed. The new distribution outperformed the exponential distribution, the Pareto distribution, the Chen distribution, and others in the field of actuarial risk analysis. Some useful key risk indicators are considered and analyzed to analyze the risks and for comparison with the competitive model. Several actuarial risk functions and indicators are evaluated and analyzed using the U.K. insurance claims data set. The process of risk assessment and analysis was carried out using a comprehensive simulation. For the purposes of distributional validity, a modified chi-squared type test is presented and employed in the testing process. The new, modified chi-squared type test that is used is simply an extension of the Rao–Robson–Nikulin test. In this work, the distributional validity is presented and analyzed under right-skewed censored and uncensored data sets.