In this paper, we present recurrence relations for moments of lower generalized order statistics within a general form of doubly truncated distributions. Characterizations for the general form of doubly truncated distributions are studied. This the general form of distributions includes distributions such as doubly truncated inverted Weibull, inverted Gompertz, generalized logistic, Burr type X, Burr type XII, logistic, inverted Pareto, inverted compound Weibull, Gumbel and compound Gompertz, among others. Doubly truncated inverted Weibull, log-inverse generalized Weibull and inverted Pareto distribution are given as applications to illustrate the results.

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In this paper, order statistics from independent and non-identically distributed (INID) random variables is used to obtain ordered ranked set sampling (ORSS). Bayesian inference of unknown parameters under a squared error loss function of the Pareto distribution are determined. We compute the minimum posterior expected loss (the posterior risk) of the derived estimates and compare them with those based on the corresponding simple random sample to assess the efficiency of the obtained estimates. Two-sample Bayesian prediction for future observations are introduced by using SRS and ORSS for one-and m-cycle. A simulation study and real data are applied to show the proposed results.

This paper deals with predicting censored data in a general form for the underlying distribution based on generalized progressive hybrid censoring scheme. A conjugate prior is used and the predictive reliability function is obtained in the one-sample case. The special case of linear exponential distributed observations is considered and completed with numerical results.