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In many experiments about lifetime examination, we will faced on restrictions of time and sample size, which this factors cause that the researcher can’t access to all of data. Therefore, it is valuable to study prediction of unobserved values based on information of available data. in this paper we have studied the prediction of unobserved values in two status of one-sample and two-sample, when the parent distribution is the exponential distribution and imposed restriction is double censoring. in each case the interval prediction by given cover will be obtain. Finally, a numerical example is given to illustrate the procedures.

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According to the first nth observations of the upper record from exponential distribution, in this article, we can compute maximum likelihood estimation of this distribution parameter. We, then, concentrate on point prediction of the future upper record values in exponential distribution based both on classic and Bayes approaches and second degree and linex loss functions.We, ultimately, deal with numerical comparison available point predictions through Monte Carlo simulation.

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‎Information inequalities have many applications in estimation theory and statistical decision making‎. ‎This paper describes the application of an information inequality to make the minimax decision in the framework of Bayesian theory‎. ‎In this way‎, ‎first a fundamental inequality for Bayesian risk is introduced under the square error loss function and then its applications are expressed in determining asymptotically and locally minimax estimators in the case of univariate and multivariate‎. ‎In the case that the parameter components are orthogonal‎, ‎the asymptotic-local minimax estimators are obtained for a function of the mean vector and the covariance matrix in the multivariate normal distribution‎. ‎In the end‎, ‎the bounds of information inequality are calculated under a general loss function‎.