The Distribution of the Number of Claims in the Third Party’s Motor Liability Insurance

In the automobile insurance tarification consists of two stages. The first step is to determine the net premiums on the basis of known risk factors, called a priori ratemaking. The second stage, called a posteriori ratemaking is to take into account the driver's claims history in the premium. Each step usually requires the actuary's selection of the theoretical distribution of the number of claims in the portfolio. The paper presents methods of consistency evaluation of the empirical and theoretical distributions used in motor insurance, illustrated with an example of data from different European markets.