The Properties And Applications For Extended Birnbaum-Saunders Distribution

Leiva proposed the extended Birnbaum-Saunders distribution based on BS distribution.The extended BS distribution is not very sensitive to outliers,it is used to air pollution and water pollution problems.This paper studies the special extended BS distribution with three parameters(denoted as EBS(?,?,?)).In actual life experiments,due to the limitation of time and financial resources,it is impossible to gain entire sample data,censoring of type dates are often selected for research.The paper concentrates on the properties and parameter estimations under censoring samples of EBS(?,?,?)distribution.The origin and its basic functions of EBS(?,?,?)distribution are given in this paper.The influences of density function of EBS(?,?,?)distribution are analyzed based on different parameters,the density function has the shape of “inverted bathtub”or “M”.The shapes of the hazard rate function are discussed under different situations.And its basic properties are also given,for example expectation and moment.The maximum likelihood estimation(MLE)and Bayesian(Bayes)estimation of EBS(?,?,?)distribution's parameters are derived when datas are complete.Under the assumption of EBS(?,?,?)distribution and BS distribution,by combining with two sets of real datas,the MLE of the parameter? mean square errors(MSE)and confidence intervals(CI)are simulated.The result shows that EBS(?,?,?)distribution has better p value than the BS distribution,which shows that EBS(?,?,?)distribution is more suitable for simulating the data.The estimations of MLE are used as starting values to obtain the Bayesian estimation.Estimation values from two methods are basically the same,but the MSEs of the Bayesian estimation are less and the CIs length are shorter than those of the MLE.The MLE and Bayes estimation of EBS(?,?,?)are explored based on the progressive censoring of type-?(PC-?)samples.Two groups of real datas are simulated by the Monte Carlo(MC)technique to illustrate the feasibility of the estimation methods.The simulation results show estimation of MLE and Bayesian estimation from the different PC-? samples are mainly the same.In most cases,the MSEs obtained by MLE are higher and the CIs length are longer than those by Bayesian estimation.