The Weibull distribution is extensively useful in the field of finance, insurance and natural disasters. Recently, It has been considered as one of the most frequently used statistical distributions in modelling and analyzing stock pricing movement and uncertain prediction in financial and investment data sets, such as insurance claims distribution. It is well known that the Bayes estimators of the two-parameter Weibull distribution do not have a compact form and the closed-form expression of the Bayes estimators cannot be obtained. In this paper and the Bayesian setting, it is assumed that the scale parameter of the Weibull model has a gamma prior under the assumption that its shape parameter is known. A simulation study is performed using random claims amount to compare the performance of the Bayesian approach with traditional maximum likelihood estimators in terms of Root Mean Square Errors (RMSE) and Mean Absolute Error (MAE) for different sample sizes, with specific values of the scale parameter and shape parameters. The results have been compared with the estimated result via the maximum likelihood method. The result revealed that the Bayesian approach behaves similarly to the maximum likelihood method when the sample size is small. Nevertheless, in all cases for both methods, the RMSE and MAE decrease as the sample size increases. Finally, applications of the proposed model to the insurance claim data set have been presented.

Deposit insurance systems are designed to balance the benefits of preventing bank runs and protecting ordinary savers against the costs of reduced market discipline and potential burdens on taxpayers. Design flaws of deposit insurance make the benefits too low and the costs too high. This paper presents an example in which solvent banks can effectively manage runs, depositors discipline banks to a reasonable extent, and taxpayers have a fair deal. It has three key features: the bank’s authority to activate deposit insurance early, a coinsurance scheme that transfer money from those who run on solvent banks to those who stay put, and a shareholder position for taxpayers. Early activation of deposit insurance prevents fire sales of assets and provides opportunities to verify the bank’s solvency. The coinsurance scheme weakens the incentive to run and strengthens the incentive to hold on to their accounts. As shareholders, taxpayers receive dividends in normal times in exchange for large payouts in catastrophic events.