Recently, analysis of the insurance claims data with outliers has achieved considerable attention for insurance indus-tries. In this regard, this paper introduces a methodology based on the contaminated lognormal distribution as an appropriate platform for analyzing insurance data with some levels of heavy tailed points. The Bayesian approach for computing the parameter estimates and the insurance premium is studied. In order to investigate the performance of the proposed methodology, some simulation studies are conducted by implementing the Gibbs sampler. We demon- strate that the proposed model is an appropriate and preferred model for dealing with the data with and without heavy tailed points. Finally, two examples of real insurance claim data have been analyzed to illustrate how well the con- taminated lognormal distribution with Bayesian parameter inference works. Also, this paper studies that the proposed model outperforms the other existing models in the literature.

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