Research And Application Of Heavy-tailed Distribution

The heavy tail characteristic of distributions exists generally in many field,such as marginal distributions of the economy finances,word frequency,hydroloty and meteoroloty domain and so on,high frequency time series almost all are the heavy tail.The tail of the heavy tail will carry a lot of important information,so how to descript the function of the heavy tail correctly is the key to access to this information.The phonemonen of the extreme value likes the stock data in financial data is required to be judged,resulting in the irreparable impact of the majority of investors and society.This article analyzes and compares the heavy-tailed distribution theory and the heavy-tailed estimation method based on the extreme value theory in detail.Based on their respective advantages and disadvantages,this paper proposes a new heavy-tailed estimation method and experiments and applications in new fields.The Hill estimator is an important estimation method in heavy-tailed estimation theory,but it has the shortcomings.In this paper,an improved method of Hill estimation is proposed,which improves the variance of Hill's estimator and simulates it with Matlab R2014 B.In the whole,the Av Hill's estimator is superior to the Hill's estimator method in the heavy-tailed estimator method when the ? is not equal to 1.In the field of word frequency statistics,the application of the Hill's estimator and the Av Hill's estimator show their advantages and disadvantage in practical application.The Mixed Moment estimators which is abbreviated as MM estimator in this paper is proposed which is based on the moment estimator and the maximum likelihood meanwhile and it also reduces the variance of the Hill's estimator.We use Matlab R2014 B to simulate the Hill's estimator,Av Hill's estimator and MM estimator,and find that they show different advantages and disadvantages in different data capacity.Hill estimation method has been widely used in the financial field.These three methods are used together in the stock of data changes in the value of the test,the comprehensive use of estimators.The three methods are commonly used in the stock price changes in the value of the test,the integrated use of estimates.The application of these three methods in stock data is well reflected.