This paper introduces a new extension of the exponential distribution tailored for enhanced reliability and risk
analysis. We incorporate several insurance risk indicators like the value-at-risk, tail mean-variance, tail value-atrisk,
tail variance, and maximum excess loss to significantly refine reliability risk assessments. These indicators
offer vital insights into the financial consequences of extreme risk events and potential for substantial losses. To
assess these risk indicators, we explore various non-Bayesian estimation techniques, including maximum likelihood
estimation, ordinary least squares estimation, Anderson-Darling estimation, right tail Anderson-Darling estimation,
and left tail Anderson-Darling estimation of the second order. Our approach involves a comprehensive simulation
study with varying sample sizes, followed by empirical risk analysis using these methods. We also evaluate the
applicability of the new model on two real reliability data sets. Finally, we apply the risk indicators including the
value-at-risk (VaRq), tail mean-variance (TMVq), tail value-at-risk (TVaRq), tail variance (TVq), and maximum
excess loss (MELq) to analyze reliability risk using failure (relief) and survival data. Finally, the peaks over a
random threshold value-at-risk (PORT-VaRq) analysis under the failure and survival data are presented. |
