Application Of The Analysis Of National Fire Loss Data Under The Generalized Pareto Distribution

Extreme value theory, which is used to research the statistical laws of extreme events, mainly includes two types of model:BMM model and POT model. Extreme value theory contains two common distributions:generalized extreme value distribution and generalized Pareto distribution, which respectively deal with two kinds of extreme samples. Considering the scarcity of data, we decide to use the generalized Pareto distribution to analyze our country’s fire loss data.In the application of fitting the generalized Pareto distribution, the most significant part is the estimation of the parameters. First, this paper has given a recursive expression of the probability weighted moments under the two-parameter generalized Pareto distribution, and then has deduced a general expression from the recursive expression. In addition, this paper has introduced the expression of the probability weighted moments under the three-parameter generalized Pareto distribution when p=1. Second, on the process of analyzing our country’s fire loss data under the generalized Pareto distribution, this paper has focused on two points: identification of the threshold and estimation of the parameters. This paper has obtained the threshold through the methods of the mean excess function and the Hill function, and has verified the availability of the threshold. After that, this paper has used the methods of maximum likelihood and probability weighted moments to compute the parameters of the generalized Pareto distribution. Thus, this paper could get the distribution function of the data, which are over threshold part. Last, this paper has analyzed the fitting results with the statistic graphs.