Statistical Analysis Of Type ? Three-parameter Generalized Birnbaum-Saunders Distribution

The Birnbaum-Saunders distribution(BS distribution for short)is an important fatigue life distribution model,which is widely used in product performance analysis.Then Diaz-garcia and Leiva-Sanchez extended the BS distribution to a series of generalized BS distribution families with non-normal kernel distribution.Based on such generalization,Zhu and Balakrishnan studied the BS distribution under Laplace kernel distribution.In another point of view,Owen improved the fatigue life model and proposed two kinds of three-parameter generalization about BS distribution.In recent years,the generalized BS distribution has been the focus of statisticians.Based on the previous generalization,this paper studied the three-parameter GBS fatigue life distribution(GBS distribution for short)of kernel distribution follow Laplace distribution.The first chapter briefly reviews the domestic and foreign achievements in GBS distribution research,The second chapter introduces the main properties of three-parameter GBSL distribution and the expectation,variance and existence of high-order mement of GBSL distribution.The third chapter studies the image characteristics of probability density function,failure rate function and average failure rate function of GBSL distribution,and gives the corresponding monotonic interval of each function.The theortical results are illustrated by function images under partial parameters.In the fourth chapter,the quasi-maximum likelihood method is proposed to simplify the solution of the maximum likelihood equation.Firstly The quasi-maximum likelihood method introduces the parameter ? estimation ?? separately.Then,under selected ??,it is solved based on the given likelihood equations as parameter estimation.In theory,the paper gave the existence condition of the solution of the quasi-maximum likelihood estimation method,and the uniqueness of the solution is qualitatively explained.In chapter 5,the accuracy of the theoretical tool is further verified by numerical simulation.At the same time,an empirical analysis is made based on ozone concentration data.The results show the efficiency of the new distribution model proposed in this paper.