On the contaminated exponential distribution: A theoretical Bayesian approach for modeling positive-valued insurance claim data with outliers

Analysis of the insurance data has recently been achieved considerable attention for insurance industries. This paper introduces the contaminated exponential (CE) distribution as an alternative platform for analyzing positive-valued insurance dataset with some levels of outliers. The Bayesian approach for obtaining the parameter estimates is presented. In order to check the performance of the proposed methodology, some simulation studies by implementing the Gibbs sampling are conducted. Finally, four examples of actual insurance claim data with various sample sizes have been analyzed to illustrate the superiority of the CE distribution in analyzing data and identifying outliers.