The Burr Inverse Weibull Model for Risk Analysis Under US Social Security Administration Disability Data Using Peaks Over Random Threshold Method with A Case Study in KSA

This study assesses and analyzes real disability insurance data to evaluate extreme risks using advanced statistical tools and metrics. The primary objective is to identify significant events or anomalies in the data and propose actionable strategies for managing financial risks associated with disability insurance claims. To achieve this, we utilize a range of indicators, including Value-at-Risk (VaR), Tail-VaR (TVaR), Tail-Mean-Variance (TMV), Tail-Variance (TV), Mean Excess Loss (MXL), Mean of Order P (MOO-P), Optimal Order of P (O-P), and Peaks Over a Random Threshold Value-at-Risk (PORT-VaR), are applied to identify and describe significant events or anomalies in the data. To address these risks effectively, the research explores the application of the Burr inverse Weibull (BIW) model, a well-regarded framework within extreme value theory (EVT). The study provides a structured approach for disability insurance institutions to better manage unexpected and potentially severe financial losses. Our dataset comprises n=2000 anonymized records from the Social Security Administration (SSA) disability insurance system. By analyzing the asymmetric, right-skewed nature of SSA disability insurance data through these advanced indicators, the research offers insights into the behavior of extreme events and long-tail distributions. Moreover, the percentage distribution of disability reasons in KSA for 2023 is considered. Based on this comprehensive risk analysis, practical recommendations are proposed.