A hybrid censoring is a mixture of type-I and type-II censoring schemes. It is categorized to type-I and type-II hybrid censored based on how the experiment set to terminate. In this paper, we describe the type-I hybrid censoring where lifetime variables have a two-parameters exponential distribution. BAYES estimation of unknown parameters under squared error loss function is developed. Among several methods of constructing the optimal procedures in the context of robust BAYESian methodology, we obtain posterior regret gamma minimax estimation of unknown parameters under squared error loss function. Finally, we discuss minimaxity and admissibility of the generalized BAYES ESTIMATOR under squared error loss.

Based on a given BAYESian model of multivariate normal with known variance matrix we will find an empirical BAYES confidence interval for the mean vector components which have normal distribution. We will find this empirical BAYES confidence interval as a conditional form on ancillary statistic. In both cases (i.e. conditional and unconditional empirical BAYES confidence interval), the empirical BAYES confidence interval is invariant w.r.t. the group with given confidence level. Finally the problem can be generalized for the exponential family.

In risk analysis based on BAYESian framework, premium calculation requires specification of a prior distribution for the risk parameter in the heterogeneous portfo-lio. When the prior knowledge is vague, the E-BAYESian and robust BAYESian analysis can be used to handle the uncertainty in specifying the prior distribution by consid-ering a class of priors instead of a single prior. In this paper, we study the E-BAYES and robust BAYES premium estimation and prediction in exponential model under the squared log error loss function. A prequential analysis in a simulation study is carried out to compare the proposed predictors. Finally, a real data example is included for illustrating the results.

In this paper, the estimation of a location parameter with a bounded reflected normal loss function is discussed. In estimating the normal mean θ, it is shown that the sample mean X , which is the best invariant ESTIMATOR of θ, is the only minimax and admissible ESTIMATOR among all linear ESTIMATORs cX + d.

Let X be a random variable from a normal distribution with unknown mean q and known variance  s2. In many practical situations, q is known in advance to lie in an interval, say [- m, m], for some m>0. As the usual ESTIMATOR of q, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of minimax estimation of q In this paper, by constructing a dominating class of ESTIMATORs, we show that the maximum likelihood ESTIMATOR is inadmissible. Then, as a competitor, the BAYES ESTIMATOR associated with a uniform prior on the interval [- m, m] is proposed. Finally, considering risk performance as a comparison criterion, the ESTIMATORs are compared and depending on the values taken by q in the interval [- m, m], the appropriate ESTIMATOR is suggested.

Due to budget and time constraints, the National Statistical Organizations usually design their surveys and optimize the size of samples at a larger geographical level e.g. the national level. This causes the economic researchers, planners, and decision-makers not to have access to their required data at the smaller geographical levels or in terms of some specific characteristics.In order to meet their statistical needs, the data users have resorted to the other agencies producing statistics which design their surveys and optimize size of samples at a smaller geographical level such as Ostan (province). Unfortunately this could impose a heavy cost on the country's budget, lengthen the process of data collection and dissemination and bring about the non-sampling errors with a higher proportion in the process. This paper, introducing some Small Area Estimation (SAE) methods, attempts to recommend an appropriate method, for estimating unemployment rates at the provincial level.

The choice of the best method estimation method is one of the goals in estimating parameters of the distribution. In this paper, I obtain the maximum likelihood and moment ESTIMATORs of the two unknown parameters of a burr type XII distribution. Also BAYESian ESTIMATOR of the parameter p under two different loss functions are derived. It is assumed that the parameter p behaves as a random variable has a gamma prior. Finally, numerical examples are given to illustrate some of theoretical results.