Statistical Analysis Of Fatigue Life Distribution Of LBS

The generalized Birnbaum-Saunders(GBS)distribution is a more flexible life model,which is widely used in reliability analysis for the products and has a good fitting effect.Therefore,exploring the properties of the distribution,statistical inference and parametric estimation methods have become a subject which has great theoretic and practical implications.In this paper,the GBS-Laplace(LBS)fatigue life distribution is mainly studied.Firstly,giving a very brief introduction to the background of LBS distribution.Moreover,the properties of LBS distribution,such as expectation,variance,variation coefficient,correlation coefficient,skewness and kurtosis are deduced in detail.Further,I analyze the distributions of variablesX-1 and aX(a>0).Then,the graphs of the density function,the failure rate function and the average failure rate function are studied and their shape trends are proved.Furthermore,I graph them under different parametric values with Matlab.The results show that: there are two types of density function: "upside down" and "upside down-upside down".Both of failure rate function and average failure rate function are also "upside down" and "upside down-upside down".Then,several estimation methods of parameters ??,in LBS distribution are given,including the moment estimation 1,the moment estimation 2,the inverse moment estimation,the quantile estimation,and I make a comprehensive comparison of the above methods,which show that: for parameter ?,the quantile estimation of the four methods is the best;for parametera,the method of moment estimation 2 is the best;In summary,the quantile estimatation is better.Secondly,the scale parameter ? of the LBS distribution are estimated in interval,and I also evaluate the performance using Monte Carlo simulations.The results show that this interval estimation method is not so good.Thirdly,I generalize distribution of LBS and introduce the position parameter ?.which is indicated as LBSI (?,?,?).And also,the moment estimation and quantile estimation of the parameters are given.In addition,by giving the true values of the parameters,the estimated values are obtained using the method of Monte Carlo simulations.