Weibull Distribution for claims modelling: A Bayesian Approach
Hamza Abubakar, Shamsul Rijal Muhammad Sabri
Abstract
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 distribution in modelling and analyzing stock pricing movement and uncertain prediction in financial and investment data set, such as insurance claims distribution. It is well known that the Bayes estimators of the two-parameter Weibull distribution do not have compact form and the closed form expression of the Bayes estimators cannot be obtained. In this paper and Bayesian setting, it is assumed that the scale parameter of the Weibull model has a gamma prior under that assumption that its shape parameter is known. A simulation study is performed using random claims amount to compare the performance of 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 similar 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 has been presented.