Odd Log-Logistic XGamma Model: Bayesian and Classical Estimation with Risk Analysis Utilizing Reinsurance Revenues Data

Abstract

Abstract Effective risk exposure descriptions can be made using continuous distributions. To illustrate the level of exposure to a certain danger, it is better to use a single number, or at the very least, a small set of numbers. These risk exposure numbers, which are commonly referred to as significant risk indicators, are unquestionably the output of a particular model. In this regard, five key indicators are utilized to define the risk exposure in the reinsurance revenues data. For this specific purpose we introduce a new distribution called odd log-logistic XGamma model . We estimated the parameters using maximum-likelihood method, least squares method and Bayesian method. Monte Carlo simulation study is performed under a set of conditions and controls. The risk exposure under the reinsurance revenue data was also described using five important risk indicators, including value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess loss function. These statistical measures were developed for the proposed new model.

Keywords

• Bayesian estimation
• Cullen and Frey plot
• Key risk indicators
• Lindley’s approximation
• Risk exposure
• Value-at-risk