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

Birnbaum-Saunders fatigue life distribution(BS distribution)is a distribution model proposed by Birnbaum and Saundere based on the life of mechanical parts in the 1970 s.Later,the statistical properties of the BS distribution and the estimation method of parameters were also studied.Subsequently,Owen improved the classic two-parameter BS distribution model,and proposed two three-parameter extensions of the inner monotonic function of the BS distribution.In recent research fields,BS distribution has received renewed attention due to its diversity and wide applicability when dealing with practical problems.This paper takes the type ? three-parameter GLBS distribution as the starting point,and studies the new type of distribution whose kernel is the Logistic distribution,which is recorded as the type ? GLBS distribution.Mainly analyze the statistical properties of this distribution,the image characteristics of the density function and the failure rate function,as well as the threeparameter estimation method and numerical simulation.Chapter One Introduction reviews the origin and research process of BS distribution.The second chapter discusses the failure mode of the BS distribution under the progressive stress accelerated life test.According to the inverse power law model,the I type GLBS distribution is derived,which is the research object of this article.The third chapter discusses the statistical properties of type ? GLBS distribution,the monotonicity and graphical characteristics of the density function and failure rate function.Chapter 4 introduces the parameter estimation method of Type I GLBS distribution,mainly using logarithmic moment estimation and quasi-maximum likelihood estimation methods to obtain three-parameter estimation.Chapter 5 presents the numerical simulation of parameter estimation of type ? GLBS distribution and the numerical simulation of parameters under general sequential stress.