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Abstract
The problem of predicting future generalized-order statistics, by assuming the future sample size is a random variable, is discussed. A general expression for the coverage probability of the prediction intervals is derived. Since k-records and progressively type-II censored-order statistics are contained in the model of generalized-order statistics, the corresponding results for them can be deduced as special cases. When the future sample size has degenerate, binomial, Poisson and geometric distributions, numerical computations are given. The procedure for finding an optimal prediction interval is presented for each case. Finally, we apply our results to a real data set in life testing given in Lee and Wang [Statistical methods for survival data analysis. Hoboken, NJ: John Wiley and Sons; 2003, p. 58, Table 3.4] for illustrative the proposed procedure in this paper.
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