Statistical Analysis Of The Generalized Three-parameter Type II Logistic Birnbaum-Saunders Distribution

The Birnbaum-Saunders(BS)fatigue life distribution was developed by Birnbaum and Saunders in 1969 for the fatigue life model and was studied in 1985 to determine the superiority of the BS distribution over estimated the life distribution.In 2005,Diaz-Garcia and Leiva-Sanche proposed the Generalized Birnbaum-Saunders(GBS)distribu-tion,which is superior to the BS distribution sometimes.The Generalized BS distribution has been evolving through the research of many scholars,and a number of distributions and methods that have wide applicability in dealing with practical problems are also proposed.In this paper,we take the three-parameter GBS distribution as the starting point to study the three-parameter type II GBS distribution,adopt the standard logistic distribution function as the kernel function of the distribution,then form the GLBSII distribution.This analysis examines the distributional properties of this distribution and its parameter estimation methods,focusing on the image characteristics of the density functions and failure rate functions of the distribution,the basic statistical properties,and the three-parameter estimation methods.In this paper,a generalized analysis is carried out a special GLBSII distribution which is based on the three-parameter type II GBS distribution.In this paper,a generalized analysis is carried out based on the three-parameter type II GBS distribution,represented by a special GLBSII distribution.The first chapter describes the background of the study of the BS distribution,reviews the progress from the BS distribution to the GBS distribution and the current status of its research.Chapter 2 discusses the image features including convergence and monotonicity of the density function and the failure rate function of the GLBSII distribution,and proposes a special method for the distribution based on the general method for analyzing the images of the generalized BS distribution.And properties of the distribution are also proved for it.Then,chapter 3 discusses the method of parameter estimation for the GLBSII distribution.For the estimation of the three parameters of the distribution,this paper uses inverse moment estimation and quasi-maximum likelihood estimation method to simplify the problem of solving complex maximum likelihood equations.The last chapter verifies the validity of the estimation method described in this paper by performing parameter estimation for certain simulation examples generated under representative conditions.It also shows the analytical results of the GLBSII distribution and its parameter estimation method in practical applications based on the theory and combined with real seismic magnitude data,and demonstrating that the distribution is still applicable in practical problems.