Fitting Heavy-tailed Distribution By Compositing Logistic Function With Pareto Distribution

Heavy-tailed data widely exists in our lives,such as data in the field of finance and insurance,which often exhibit their leptokurtic shape.But for this type of data,the single models can not fit extreme data well enough.Although the generalized Pareto distribution is more effective in fitting the tail data,it is difficult to describe the overall data.Therefore,in recent years,many improved composite models have been suggested,which can fit the data with high peak and fat tail better.In this thesis,we improved the Logistic function and combined it with the generalized Pareto distribution to form a new model.Taking flood loss data and stock yield as examples to fit data respectively,it proved that the fitting steps of the model are simple and the fitting effect is good.The composite model can provide new ideas for studying leptokurtic and fat tail data,and it is also of great significance to the research of risk management.The thesis can be divided into the following four parts:In the first part,we introduced some research related to extreme value theory and innovation ideas of this thesis.Since the development of extreme value theory,whether it is the theoretical research or related applied research,it has been very in-depth.On the basis of these researches,we summarized some of the shortcomings,and proposed some innovations.In the second part,we introduced the theoretical involved in the thesis.Including based on model POT under GPD,the two methods of determining the threshold in the model,the method of testing the peak and thick tail of data,and the calculation method of the stock yield.In the third part,we introduced how to improve the Logistic function and combine it with the generalized Pareto distribution to construct a new composite model and conduct empirical analysis.In the thesis,we used the POT model and the composite model to fit the flood loss data and stock yield respectively,by comparing the fitting steps and fitting effects of the two to verify the feasibility and reliability of the model in this thesis.The fourth part is a summary and reflection on the thesis.Based on the summary of the full thesis,some existing problems for current research and further improvement are proposed.