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

Birnbaum Saunders model is an important failure distribution model in probabilistic physics.BS distribution was derived by Birnbaum and Saunders in the late 1960s when they studied the failure process of materials caused by crack growth.Until the beginning of the 21st century William J.Owen argued two new three-parameter generalized BS distribution(type I and type II),abbreviated as three-parameter GBS distribution.On the basis of Owen's new type II three-parameter generalized BS distribution,this paper extends BS distribution by replacing the kernel distribution with the standard Laplace distribution(GBSL).Firstly,this paper studies the image characteristics of density function,failure rate function and average failure rate function of GBSL distribution.Secondly,this paper suggests the estimation of the parameter m by using quasi-maximum likelihood method and quasi-inverse moment estimation method respectively.In addition,this paper use the Fisher Information matrix to obtain the approximate interval estimates of the parameters m and?.In the second chapter,the image properties of density function,failure rate function and average failure rate function of GBSL distribution are studied.It is proved concretely that some characteristics of density function of GBSL distribution under different parameter values.As well,this paper obtain conclusions on the failure-rate function and average failure-rate function of GBSL distribution.Chapter 3 proves the existence of GBSL higher-order moments E(X~k)(k is any real number)and gives the theoretical basis for the median estimation of point estimation of scale parameter?.Furthermore,the uniqueness of estimation of parameter m under quasi maximum likelihood estimation method and the quasi inverse moment estimation method is proved respectively when scale parameter?(28)??is fixed.Furthermore,this paper proved the existence of estimation of parameter m when the sample data under certain conditions.In the fourth chapter,the results of quasi-maximum likelihood estimation and quasi-inverse moment estimation are simulated by Monte-Carlo simulation method.The fifth chapter makes an empirical analysis on the survival time of Guinea pigs injected with different dosage of Mycobacterium tuberculosis.