Construction,Properties And Applications For Some Mixed Statistical Models

Because of the complexity and diversity of research objects,as well as the timeliness of random sampling,it is very difficult to make a random variable meet the hypothesis of a given distribution function or density function.In the simulation of actual data,more abundant statistical distribution classes are needed,so that the new model can better describe the corresponding practical problems.In this paper,two methods are used to construct the mixed statistical model: one is the weighted sum of two distributions,and the other is based on the T-X transformation method.Then,the relevant properties of these statistical distributions are given,including the limit,unimodal,shannon entropy,moment and other application levels of the mixed distribution.The mixed model constructed by using real data is empirically analyzed and compared with other models to illustrate the advantages of the mixed model.This paper is divided into three chapters.The first chapter is the prolegomenon,which first introduces the research background and significance of this paper,then introduces the development history of the mixed model,and makes a detailed description of the research status of the mixed model,and finally gives the main work and research significance of this paper.The second chapter mainly studies the mixed model constructed by using two distributed weights.The first section introduces the construction process of the Exponentiated Exponential-Pareto(?)mixed model and the corresponding statistical properties.And we use the Danish fire loss data for fitting analysis.In the second section,we construct mixtures of Burr and log-normal distributions.Some related statistical properties are investigated.And the fitting analysis of the Burr and log-normal mixed model is made by using the direct economic loss data of 31 provinces and cities in China from 1999 to 2012,indicating the advantages of the fitting of the Burr and log-normal mixed model.In chapter 3,the T-X transformation technique is used to construct the mixed distribution and study its properties.The first section considers the exponentiated Weibull-Pareto distribution,obtains various properties of the distribution,and conducts an empirical analysis using the fatigue life data of 6061-T6 aluminum.The second section constructs the Weibull-Pareto(?)distribution,studies its related statistical properties,anduses the 6061-T6 aluminum data and the Wheaton River data of Canada for fitting,indicating that the Weibull-Pareto(?)distribution fitting effect is better.