Statistical Analysis of Natural Events in the United States

Abstract A statistical analysis is performed on natural events which can produce important damages to insurers. The analysis is based on hurricanes which have been observed in the United States between 1954 et 1986. At first, independence between the number and the amount of the losses is examined. Different distributions (Poisson and negative binomial for frequency and exponential, Pareto and lognormal for severity) are tested. Along classical tests as chi-square, Kolmogorov-Smirnov and non parametric tests, a test with weights on the upper tail of the distribution is used: the Anderson – Darling test. Confidence intervals for the probability of occurrence of a claim and expected frequency for different potential levels of claims are derived. The Poisson Log-normal model gives a very good fit to the data.