A novel XGamma extension: applications and actuarial risk analysis under the reinsurance data

Continuous distributions can be used to characterize risk exposure successfully. It is preferable to use a numerical value, or at the very least, a limited selection of numbers, to show the degree of exposure to a particular threat. These risk exposure figures, often known as major risk indicators, are indisputably a specific model's output. The risk exposure in the reinsurance revenues data is defined in this study using five important indicators. We create a new XGamma extension specifically for this use. The maximum-likelihood method, maximum product spacing, and least square estimation were used to estimate the parameters. Under a certain set of circumstances and controls, a Monte Carlo simulation study is carried out. Five crucial risk indicators, including value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess loss function, were also used to explain the risk exposure in the reinsurance revenue data. These statistical measurements were created for the new model that was provided.