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The traditional automobile insurance bonus-malus system (BMS) merit-rating depends on the number of claims. An insured individual who makes a small severity claim is penalized unfairly compared to an insured person who makes a large severity claim. A model for assigning the bonus-malus premium was proposed. Consideration was based on both the number and size of the claims that were assumed to follow a Poisson-Lindley distribution and a Lognormal-Gamma distribution, respectively. The Bayesian method was applied to compute the bonus-malus premiums, integrated by both frequency and severity components based on the posterior criteria. Practical examples using a real data set are provided. This approach offers a fairer method of penalizing all policyholders in the portfolio. Key-Words: Automobile insurance, Bayesian method, Bonus-malus system, Claim severity, Number of claims, Poisson-Lindley distribution, Lognormal-Gamma distribution Received: Revised: Accepted: Published:

Bayesian Bonus-Malus Premium with Poisson-Lindley Distributed Claim Frequency and Lognormal-Gamma DistributedClaim Severity in Automobile Insurance