The increased risk of accidents that occurred in motor vehicles also create increased competition among direct car insurance companies. Insurance companies offering various systems to attract the public to become policy holders in insurance companies. No-claim bonus is one of the systems offered by direct car insurance companies. In this system the amount of premium is influenced by the amount of the claim made by a person policyholders in the past year in case of accident.
if no accidents were reported on a period of one year, the state will be reduced as much as one and for any accidents reported to rise as much state s.
Determination of state in the no-claim bonus system based on a search for Poisson distribution which states the number of accidents reported or the number of claims each year. The final results obtained from the search with this Poisson distribution that determines the percentage of premium payment in each state, state transfer rules and financial analysis for the company concerned. This affects the policyholder to make a claim or not to make a claim against any damage that occurs in an accident
Previous research by Mert and Sykan (2005) set the premium to be paid in subsequent years depending on the amount of the claim made and the value of the previous year. The number of claims is determined by Poisson distribution, the number of expectations with an exponential distribution and the value of the claim with the exponential distribution is modeled using Gamma distribution, so that the claim sizes follow Pareto distribution
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