Estimation Of Change Points Of Shape Parameters Of Pareto Distributions

The change-point problem was first proposed by Page in the middle of 1950 s.With the development of change-point estimation in recent years,it has become a research hot issue.At the same time,many scholars have intensified theoretical and applied research on it.The change point research has been rapidly developed.The Pareto distribution was first proposed by Vilfredo Pareto in the late 1890 s.Later,some scholars found that the Pareto distribution has a wide range of applications in various fields.Therefore,Pareto distribution has been improved and extended to several kinds of Pareto distribution,which formed Pareto Distribution Family.Next,we will mainly study the estimation of the change-point positions of the shape parameters of the two special distributions in the Pareto distribution family.Firstly,it briefly describes the domestic and foreign research background on the change-point problem and the Pareto distribution family,and the theoretical basis of maximum likelihood estimation and Bayesian estimation are introduced one by one.Secondly,the basic theoretical knowledge of Pareto distribution family is introduced,and by using the Bayesian method and the maximum likelihood estimation method,the shape parameter of the Pareto distribution family is used to establish the model of the change point m.At the same time,these two estimation methods are used to deal with two specific distribution change-point in the Pareto distribution family,namely the Pareto distribution and the Lomax distribution.In the process of using the Bayesian method to estimate,two prior distributions are used to obtain the full conditional distribution of the parameters of the distribution.Then,using the maximum likelihood estimation and the MCMC algorithm and the IBF algorithm in the Bayesian method,respectively,random simulations were performed on the change-point of the Pareto distribution and the Lomax distribution.Through random simulation,it is found that the simulation result of Bayesian method is closer to the real value in the parameter simulation result,and the Markov chain generated by the MCMC algorithm in the simulation process is convergent,indicating that the simulation results are very ideal.At the same time,the simulation results of the IBF algorithm are not much different from the MCMC algorithm,but the IBF algorithm has the advantage of faster calculation speed compared to the MCMC algorithm.Finally,this article is summarized,some conclusions and prospects are made for the change-point estimation,and the areas that need to be further improved are listed.