The Log-Exponentiated Polynomial G Family: Properties, Characterizations and Risk Analysis under Different Estimation Methods

This work presents a new class of probability distributions termed the Log-Exponentiated Polynomial (LEP) G family. We explore its fundamental properties and provide characterizations. The paper focuses on risk analysis using different estimation methods. The LEP G family offers flexibility for modeling various data types. We derive useful expansions for the new family, these expansions facilitate the calculation of moments and other statistical measures. The model’s parameters are estimated using several methods, including Maximum Likelihood Estimation (MLE). We also employ Cramer-von Mises (CVM), Anderson-Darling (ADE), Right Tail Anderson-Darling (RTADE), and Length Bias Extended (LEADE) estimation techniques. A simulation study evaluates the performance of these estimation methods. Bias, Root Mean Square Error (RMSE), and Anderson-Darling distance metrics are assessed. The LEP Weibull model is applied to insurance claims data for risk measurement. Key Risk Indicators (KRIs) like Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR), Tail Variance (TV), Tail Mean Variance (TMV) and Expected Loss (EL) are calculated. We also analyze artificial data to demonstrate the model’s behavior under controlled conditions. The results highlight the impact of different estimation techniques on risk assessment. The LEP G family proves to be a robust and adaptable framework. It provides a valuable tool for statisticians and actuaries in modeling complex datasets. This work contributes to the advancement of distribution theory and its practical applications.