A New Heavy-Tailed Lomax Model With Characterizations, Applications, Peaks Over Random Threshold Value-at-Risk, and the Mean-of-Order-P Analysis

In this work, a new heavy-tailed Lomax model is proposed for the reliability and actuarial risk analysis. Simulations are conducted to investigate how the estimators behave. Parameters are derived through maximum likelihood estimation techniques. The efficacy of the newly proposed heavy-tailed Loma distribution is illustrated using the USA indemnity loss datasets. The findings clearly indicate that the new loss model offers a superior parametric fit compared to other competing distributions. Analyzing metrics such as value-at-risk, tail mean variance, tail variance, peaks over a random threshold value-at-risk (PORT-VAR), and the mean-of-order-P (MOP(P)) can aid in risk assessment and in identifying and describing significant events or outliers within the USA indemnity loss. This research introduces PORT-VAR estimators tailored specifically for risk analysis using the USA indemnity loss dataset. The study emphasizes determining the optimal order of P based on the true mean value to enhance the characterization of critical events in the dataset.