Asymptotics Properties Of Extremes From Birnbaum-Saunders Distribution

The asymptotic properties of extremes from a sequences of Birnbaum-Saunders distribution are discussed in this thesis.Let {Xn,n≥1} be a sequence of inde-pendent and identically distributed random variables with Birnbaum-Saunders dis-tribution.Let Mn=max{X,1≤i≤n},mr(n)is the r-order moment of the distribution of Mn,and Mnt is the power of Mn.In this article,the asymptotic ex-pansion of the distribution of Mn and mr(n)is discussed,as well as the asymptotic expansion of the distribution function and the density function of Mnt is givenThe thesis is divided into four parts:In the first part,we derive the asymptotic expansion of the distribution function of Mn as well as the associated convergence rate are derived.In the second part,the asymptotic expansion and convergence rate of mr(n)is given.In the third part,the asymptotic expansion and convergence rate of the distribution function and the density function of Mnt are obtained.In the fourth part,based on the theorems proved by the first part and the third part,the numerical simulation analysis is carried out.The effect of asymptotic expansion of Birnbaum-Saunders distribution is evaluated by comparing the actual values,the first-order asymptotic,the second-order asymptotic and the third-order asymptotic.