We introduce an innovative compounded loss model, which integrates features from the Xgamma and exponential distributions to effectively capture the intricate distributional patterns observed in insurance loss data. A key focus of our study is an extensive empirical investigation that evaluates the Mean-of-Order-P ( \(\hbox {MO}^{(P)}\) ) approach within the new compounded loss framework. Through comprehensive simulations using a large dataset and varying P from 1 to 50, we rigorously examine the ability of the empirical moments to capture higher-order statistical characteristics. This empirical study not only confirms the effectiveness of the \(\hbox {MO}^{(P)}\) but also provides valuable insights into its practical application across different orders of P. Further, we explore the practical utility of the proposed approach and the peaks over random thresholds Value-at-Risk (PORT-VaR) analysis specifically within the context of USA insurance losses. By applying these methodologies, insurers can assess and manage their exposure to extreme events more effectively, thereby bolstering their risk management strategies and ensuring financial stability. In this context, we present some mathematical properties of the new distribution along with a simulation study to evaluate some classical estimation methods with two applications, one in medicine and the other in reliability.
