distributional nikulin-rao-robson validity under a novel gamma extension with characterizations and risk assessment

In this work, a novel probability distribution is introduced and studied. some characterizations are presented. several financial risk indicators, such as the value-at-risk, tail-valueat-risk, tail variance, tail mean-variance, and mean excess loss function are considered under the maximum likelihood estimation, the ordinary least squares, the weighted least squares, and the anderson darling estimation methods. these four methods were applied for the actuarial evaluation under a simulation study and under an application to insurance claims data. for distributional validation under the complete data, the well-known nikulin-rao-robson statistic is considered. the nikulin-rao-robson test statistic is assessed under a simulation study and under three complete real data sets. for censored distributional validation, a new version of the nikulin-rao-robson statistic is considered. the new nikulin-rao-robson test statistic is assessed under a comprehensive simulation study and under three censored real data sets.