Weibull-discrete Phase Type Distribution

Life distribution is one of the key research contents of statistical distribution,and it is the basis for reliability research and reliability engineering.In the fields of medicine,biology and insurance,the life of people or organisms should be analyzed,and the reliability of machines and products should be studied in industrial production,which can't be separated from the distribution of life.With the rapid development of science and technology,new materials and new products emerge in an endless stream.The reliability of products has increasingly become the focus of attention.The existing life distribution can no longer meet people's needs,so a variety of mechanism of life distribution is proposed,which provides great convenience for the study of life data.In this thesis,a new class of lifetime distributions with various shapes,named Weibull-discrete phase-type distribution which is obtained by compounding Weibull distribution and discrete phase-type distribution is introduced.The statistical properties,parameter estimation and hypothesis testing of the distribution are studied.In the first chapter,the research background and current situation are introduced,and the discrete phase distribution is briefly introduced.Chapter 2 gives the definition of the Weibull-discrete phase distribution,and obtains the expression of the density function,distribution function,the hazard rate function,the kth momen and the con-ditional expectation.Chapters 3 and Chapters 4 study a special Weibull-discrete phase distribution:Weibull-geometric distribution order 2.In chapter 3,the properties of the density function and hazard rate function of the distribution are studied.In chapter4,the consistency and asymptotic normality of the maximum likelihood estimation of the distribution and the K-S test and likelihood ratio test of the distribution are given.In chapter 5,the numerical simulations of point estimation and interval estimation of the parameters of Weibull-geometric distribution order 2 are given.Chapter 6 uses Weibull-2 order geometric distribution to fit two groups of real data in order to reflect its practicality.