A Bayesian Approach to Weibull Distribution with Application to Insurance Claims Data

Statistical distributions are of great interest for actuaries in modelling and fitting the distribution of various data sets. It can be used to present a description of risk exposure on the investment, where the level of exposure to the risk can be determined by “key risk indicators” that usually are functions of the statistical model. Financial mathematicians and actuarial scientists often use such key risk indicators to determine the degree to which a particular company is subject to certain aspects of risk, which arise from changes in underlying variables such as prices of equity, interest rates fluctuations, or exchange rates. Weibull distribution is one of the most popular statistical distribution models employed by the actuarial and financial risk management problems in fitting and or in modelling the behaviours of financial data or lifetime event data to forecast stock pricing movement or uncertainly prediction. In this study, a Bayesian approach to the Weibull distribution model on the assumption of gamma prior to Weibull distribution parameters has been proposed. A computational study based on the actuarial measures is conducted, proving the proposed distribution of the claim amount. Along this line, in assessing the performance of the proposed method, the results of the simulations study have been conducted to explore the efficiency of the proposed estimators is compared to a maximum likelihood (MLE) and simulated annealing algorithm (SA). Finally, an actuarial real data set is analyzed, proving that the proposed model can be used effectively to model insurance claim data.