Distribution Fitting Based On Heavy - Tailed Property Claim Data

With rapid economic development, the risk continues to expand, the insurance industry rapidly develops into a global industry. In recent years, with rapid China’s economic development, non-life insurance begins to grow rapidly. At the same time,the development of the insurance industry has made more stringent requirements for the regulation of the insurance industry, so designing a reasonable premium rate is particularly important, as designing insurance rate is base on fitting distribution of claims data.This paper mainly presents the composite lognormal-Pareto model, mixture lognormal-pareto distribution and several common claims distribution, and fitting respectively property insurance claims data of nearly five years. While using maximum likelihood method and EM algorithm to estimate the unknown parameters in the models. Then, the NLL, K-S statistic, AIC, BIC criterion to compare several distribution’s fitting effect in different years. As can be seen, the models have different advantage in the real data in different years.