Research On Fitting Models In The Loss Distribution Of Medical Insurance

In foreign countries, commercial medical insurance actuarial study has been relatively mature with the development of mathematics and statistics. Insurance corporations have accumulated data. The models relatively sophisticated have been used in Pricing, distilling the reserve, actuarial regulatory and risk control. In China, Commercial health insurance developed from the early 1980's, after over 20 years'development, the size, quality and level of the health insurance industry have improved greatly. However there exist a lot of problems which we have to deal with. For instance, currently, the supply and demand have been good for commercial health insurance, but Business is not satisfactory.Facing such problems, not only could we do is establishing correlative policy but also using the actuarial technique. The loss distribution of health insurance is the foundation of health insurance actuarial. So it's great meaning that we study the loss distribution. In the thesis, we studied the methods about loss distribution on health insurance and introduced the process by the numbers.The thesis is divided into three chapters, the main content and viewpoints as follows:First, Preface. In the preface, the background, content and meaning about the research is introduced and then a Literature Review. Loss distribution on health insurance has important practical and theoretical significance. It is the basis of pricing and reserve, playing a decisive role in the rational pricing. To carry out effective monitoring of health insurance, loss distribution of health insurance must be studied.Chapter 2 is about the kinds of mean which fit the loss distribution.This chapter, first, teaches us how to deal with the data, draw P-P and Q-Q charts. Then it introduces the ways searching loss distribution including parametric and nonparametric.The department of parametric shows the family of distribution and their nature and relationship with each other covering the family of beta, the family of Gamma. From which the Gamma distribution, log-normal distribution, Weibull distribution, Pareto distribution is selected whose tails are compared carefully because of its importance. Subsequently, the models which are selected are taken goodness-of-fit test. The models'parameters passing the test are estimated by Moment Estimator, Maximum Likelihood Estimator, Quantiles estimator, Minimum Distance Estimator, Minimum chi-square Estimator, Bayes Estimator, Markov chain Monte Carlo, etc. The author describe the differences between them. When only one model could not estimate the loss distribution very well, a mixed model would be used for compensation.The department of nonparametric presents three kinds of meanings in accordance with the order of their developing, containing histogram, Parzen Kernel Density Estimator, k-neighbor method. It focuses on Parzen Kernel Density Estimator, describes the concept of kernel density, and discusses how to select bandwidth.Finally, the principles and criterion that selects the best models are summarized.Chapter 3 analyses the data from claims of Chengdu. The data is divided into 12 groups according to gender and age. Gamma distribution, log-normal distribution, Weibull distribution, Pareto distribution, Kernel Density Estimation are used to fit the distribution of claim data and chi-square test is used to test the goodness-of-fit.Contribution and characteristics of this paperFirst, in this paper, health insurance loss distribution is researched systematically. It concludes all of the fit means almost.Second, this paper focuses on the combination of theory and practice. Its results give Chengdu's loss distribution about health insurance great inspiration.Third, it introduces the Kernel Density Estimation, which is rare in domestic.