Statistical Analysis On Heteroscedastic Normal-pareto Mixture Model And Its Application

Pareto distribution was initially explicitly introduced as an income distribution,and s-ince then was further studied by more and more researchers.Because of its thick tail,both shape and scale parameters,Pareto distribution has been widely applied in numerous fields at present,such as extreme value analysis,surviving analysis,reliability study,financial risk management fields and many more.In particular,the Pareto Type II distribution which is the development of the classical Pareto distribution,has been widely discussed for its outstanding properties in study.In the classical statistical inference,it is usually assumed that the data comes from a single distribution.However,in the actual situation,the generation of data is usually very complex,and not just following a single distribution.The finite mixture distribution provides a mathematical method for a large class of random phenomena,which could not be explained in the past.Besides,the finite mixture distribution which can be applied in many fields has been proved to be a flexible and mighty statistical modeling technique.The finite mixture model also has a good effect in accounting for unobserved heterogeneity.A large number of researches for the models focus on the parameter estimation in recent years.Many studies have been dexeploted for the expectation but not the analysis of variance.However,with the development of the diversity of data,the data needs to be interpreted more in depth.Hence,it has theoretical and practical significance to study the finite mixture model with Pareto distri-bution,which is becoming one of the hot issues discussed in the modern statistical analysis.We mainly consider a finite mixture model with the existing data structure in this work.In this dissertation,we use different methods to estimate the parameters in mixture of distri-butions,including joint modeling of the mean and variance with covariates.Some important properties of the mixture have been discussed and some advantages of this mixture have been proved by the real data application.Specifically,this research’ s contents of this dissertation are summarized as follows:Firstly,the mixture distribution of normal-pareto is proposed,and the mathematical ex-pectation and variance of the mixture distribution are combined to establish the model.In the investigation of the basic properties of the model,it is found that the model appears a lot of advantages compared with the similar model.And it is also found that this new mixture dis-tribution has a special hazard function.In addition,in order to facilitate the following study,latent variables are introduced.Secondly,based on common EM algorithm,we try to extend the MCMC algorithm with Bayesian theory.The Proposal distribution which is obtained by combining the prior distribution of the parameter vector with the likelihood function of the working observations variables whose joint density is assumed to be multivariate normal is convenient for sampling and fully utilized.The results of the simulation test the accuracy of the estimation.Finally,we focus on the analysis of the data feature of the covariates,,and applied it to the analysis of the actual data.The results of the analysis are well confirmed by biology data.At the same time,the estimates of the parameter related to the variance attributed to focusing and explaining the phenomena in biology,and provide attributions for the further exploration of biological problems.The results of empirical analysis illustrated that the model established in this dissertation shows some advantages compared with other existing models.