Statistical Analyses For Modified Weibull Distribution

The Modified Weibull Distribution(MWD)was expanded from the Weibull distribution which is used in reliability statistics inference.For Weibull,the failure rate can be increasing and decreasing,but for MWD,the failure rate not only be increasing,but can be bathtub shaped curve.In reliability analysis,the censored life testing is often adopted by experimenter in order to save costs and time.In this paper,the maximum likelihood estimation(MLE)and the Bayesian estimation for parameters,reliability and failure rate of the MWD are investigated under generalized progressive censoring of type-?(GPC-?)samples.Firstly the concept of reliability,failure rate,property are derived.Secondly,the two parameters of the MWD are discussed by using MLE and Bayes methods under GPC-? sample.For the Bayesian estimation,we investigate the point and credible intervals of the parameters,reliability and failure rates using the Lindley approximation and the MCMC simulation.Then,the three parameters of the MWD are estimated based on the MLE and Bayesian methods.Under the MLE,the confidence intervals are obtained by Fisher observation information matrix and Bootstrap method.And for Bayesian estimation,the M-H sampling method and the G-M sampling method are used to obtain the parameters,reliability,failure rate,and the corresponding credible intervals.Finally,the precision of parameter estimates are compared based on square error.Numerical simulation results shown that Bayesian estimation is better than MLE when sample size is small;the Bayesian estimations under prior information are better than that nonprior information;the G-M sampling method is more efficient than the M-H sampling method;the highest posterior credible intervals is more reasonable than the progressive normal distribution confidence intervals;Compared with Lindley approximation,G-M and M-H methods have higher adaptability and precision for MWD.