Statistical Analysis Of Exponentiated Weibull Distribution

This paper studies the exponentiated Weibull distribution which was introduced by Mudholkar and Srivastava (1993). The characteristic of the distribution is that its density is unimodel and its hazard function can be increasing, decreasing, in bathtub shape.The following are discussed in this paper:(1) The origin moments, percentiles and mode of exponentiated Weibull distribution are introduced and different forms of hazard functions under different value of pa-rameters are discussed.(2) Three methods of estimation of the exponentiated Weibull distribution are dis-cussed, i.e. the inverse moment estimation(IME), the maximum likelihood estima-tion(MLE) and the Bayes estimation(BE).(3) Comparisons are done for the inverse moment estimation, maximum likelihood esti-mation and Bayes estimation for the single parameter and two-parameter exponen-tiated Weibull distribution through numerical simulation, based on the criteria of mean square error(MSE). The results show that the Bayes estimation performs bet-ter than the inverse moment estimation and the maximum likelihood estimation for small samples. And the inverse moment estimation performs better than the max-imum likelihood estimation and the Bayes estimation for large samples. Besides, numerical simulation is applied for the three-parameter exponentiated Weibull dis-tribution through the Metropolis and Gibbs sampling, with the ergodic mean as the Bayesian estimates of the unknown parameters, which are then compared with the maximum likelihood estimates.