Non-life Insurance Loss Data Tail Distribution Of The Non-parametric Statistics

In this paper,a new method of tailed distribution research has been presented by employing the nonparametric density estimation based on we pay a detailed study of the traditional non-life insurance losses tailed modeling based on statistical extreme value theory. As the object of this paper is the statistical regularity of the non-life insurance loss data tailed.We need to think of how to divide a reasonable tailed region,that is to say how to select a appropriate threshold,before we use the nonparametric density estimation method to model the tailed distribution.The first part of the theoretical and empirical analysis in the paper, we focus on the discussion of the issue of threshold selection in depth.By using a Bootstrap method to choose the threshold this paper described, then we can get a certain threshold,we demonstrate the reasonableness of this threshold after which is compared with two results arising from the two traditional graphic ways of choosing threshold which mechanisms are relatively subjective.We attach importance to the introduction of two sort of nonparametric density estimation techniques and three kind of smoothing parameter selection methods and algorithm theory in the second theoretical research parts.In the second empirical analysis we take advantage of three different means of smoothing parameter selection for the nonparametric kernel density estimation to aquire three specific density estimator of the tailed distribution,and then we consider the density estimators' risk that is the integrated mean squared error of the estimator as the evaluation criteria so that we find out the best approximation of the density of the tailed popularity by means of selecting cross-validation smoothing parameter.In the last section we exemplify how to utilize the threshold result of the first empirical analysis and the density estimator result of the second empirical analysis to calculate the net premiums of the stop loss reinsurance.