Evaluating how data of “retention limits for saudi insurance market” fits a progressive type-ii censored sample for weibull generalized exponential distribution

Aims: The main aim is to determine the optimal orientation of retention rates and then determine reinsurance shares for the various insurance branches in the Saudi insurance market by building statistical modelling with model parameters by which risk factors can be monitored according to the insurance branch, as well as forecasting growth or possible contraction in retention rates by Insurance branch in the Saudi insurance market. Place and Duration of Study: Retention rates by insurance activity in the Saudi insurance market for the year 2018 and up. Methodology: Weibull Generalized Exponential distribution parameters based on censored samples have been discussed by using Maximum Likelihood, Bayesian Estimation based on the Markov Chain Monte Carlo method. Results: An increase in the risk factors for instability in the retention rates with the most extreme values, whether the rate is more extreme, increased, or decreased. Represented in branches; Health insurance, Energy insurance, Vehicle insurance, Protection and savings, an increase in the rate of retention for branches; Energy insurance and Aviation insurance, insurance branches whose retention rate is expected to decrease are Health insurance followed by Vehicle insurance, Bayesian Estimation is better and more efficient than the MLE and MPS estimation. Conclusion: In approximately most of the situations, we notice that the measures of Bayesian estimates are preferable than the measures of MLE estimates. As the data of retention limits by activity in the Saudi insurance market are fitting to the model and how the schemes work in practice, effectiveness in determining retention limits “Reinsurance” ensures balanced financial performance and stable profitability level