Reconstruction Order Statistics in Middle Censored Data

Let Y1; ; Yn be order statistics from a distribution with parameter . Assume that someof middle order statistics are lost, that is we only observed the data set Y = fY1; ; Yr; Ys; ; Yng. Weare going to reconstruct the l(r < l < s)th order statistic based on the data set Y. In this work, we proposetwo methods: Maximum Likelihood Reconstruction(MLR) and Bayesian Reconstruction(BR). To computeMLR, we obtain closed form for reconstruction Yl. The next method for reconstruction Yl is the Bayesianapproach. In this approach, we assume that the unknown parameter is viewed as the realization of arandom variable which has a prior distribution. A numerical method has to be applied to compute the BR.Also, numerical example and Monte Carlo simulation study of the L evy distribution are given to illustrateall the reconstruction methods discussed in this work. To evaluate the estimators, we compute Mean SquareReconstruction Errors for the MLR and BR reconstructions. Finally, we conclude BR is better than MLR.

کلیدواژه ها:

Bayesian Reconstruction ، Levy distribution ، Maximum Likelihood Reconstruction.