| The extensive application of Pareto distribution and its excellent properties have attracted more and more attention of researchers. Some previous studies have mainly studied the various methods of parameter estimation in this distribution, and make a relatively complete conclusion. The research on interval estimation is very little. In this paper, we make a deep discussion and give some methods to solve the interval estimation, and make a comparison between these methods. Finally, we make a statistical analysis of the properties of the parameters from the point of view of hypothesis testing.The first part simply introduces the development background of Pareto distribution and the research status of parameter estimation, points out the research direction of this paper, and explains the whole structure of this paper.In the second part, we introduce the basic concepts involved in the hypothesis test, and discuss the excellent performance of these tests in a given "good or bad" standard, to study whether there is an optimal test method, and how to solve the problem in the presence of Pareto distribution. This chapter illustrates the UMPT solution of two kinds of unilateral hypothesis testing problems.The third part mainly introduces the concept of interval estimation and the solution of various theoretical methods, including the pivot method, the asymptotic normality of the maximum likelihood estimation method and the two approximation method, and the most accurate confidence interval, and the average length of the interval as short as possible. Finally, the accuracy of the interval estimates obtained by these methods are compared. The Pareto as an example illustrates the effectiveness and the use of these methods.In the fourth part, the connection and difference between interval estimation and hypothesis testing are introduced, and the problem of hypothesis testing and interval estimation is illustrated by Pareto distribution. Finally, the research topic is prospected. |
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