A Class Of Generalization For Birnbaum-Saunders Distribution

Birnbaum-Saunders distribution is a new fatigue life model proposed by Birnbaum and Saunders when they studied the failure of parts caused by the continuous accumulation of dominant cracks,called the BS distribution.Whereafter,in the 1980s,Desmond proposed that BS distribution is an equal-weight mixture of inverse Gaussian distribution and complementary reciprocal distribution.Based on the mixed properties of BS distribution proposed by Desmond,this paper extends the classical BS distribution with the generalized inverse Gaussian lifetime distribution,and proposes a new class of generalized BS distribution,also known as the generalized BS distribution.The cumulative distribution function,probability density function and hazard function of these new distributions are studied,and the estimation methods of parameters are discussed.Combined with numerical simulation,the model is evaluated.In chapter 2,the basic statistical properties of generalized BS distribution are given,and the function images of distribution function and density function are obtained.In the third chapter,statistical inference is made and the point estimation of parameters is obtained by using EM algorithm.The whole process of interval estimation by bootstrap method is introduced in detail.In the fourth chapter,the parameter estimation is explained and verified by numerical simulation,and the relative bias,root mean square error and 95% coverage rate are calculated.Finally,the model is validated by analyzing the continuous failure times of air conditioning system and the fracture stress of carbon fiber.