The Composite Models Based On The Exponentiated Weibull Distribution

The insurance loss data has the characterisics of leptokurtic shape,because it contains a large number of small losses and a small number of high losses,and using the single model to fit the data is generally not ideal.Considering that the exponentiated Weibull distribution has more flexible failure functions than the exponential distribution and Weibull distribution,this paper studies the composite model based on exponentiated Weibull distribution,including the exponentiated Weibull composite model,and the truncated exponentiated Weibull composite model.In this paper,it constructs the exponentiated Weibull composite model that is the exponentiated Weibull density up to an unknown threshold value and the transformed beta density for the remainder.Then the Danish fire loss data is used for empirical analysis,compared with other composite models,and the fitting advantage of the exponentiated Weibull composite model is tested.This paper is divided into four chapters.Chapter 1 is the prolegomenon,in which it firstly introduces the background and significance of the research,then it introduces the development history of the composite model with a detailed elaboration on the research status of the composite model.Finally it gives the main results of this paper.In chapter 2,it introduces the exponentiated Weibull distribution from the development history of exponentiated Weibull distribution,the definition of exponentiated Weibull distribution and the property of the exponentiated Weibull distribution,showing the advantage of using exponential Weibull distribution.In chapter 3,the exponentiated Weibull composite model is mainly studied.Firstly it introduces the construction process of the composite model,and then introduces the construction process of the exponentiated Weibull composite model and its corresponding properties.Finally,the Danish fire loss data is used to fit the exponentiated Weibull composite model and Weibull composite model,the results show the fitting advantage of he exponentiated Weibull composite model.In chapter 4,the truncated exponentiated Weibull composite model is mainly studied.Firstly it introduces the construction process of the truncated composite model,and then introduces the construction process of the truncated exponentiated Weibull composite model.Finally it uses the Danish fire data to fit the truncated exponentiated Weibull composite model,showing the advantage of the truncated exponentiated Weibull composite model.