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The problem of predicting the rth ordered observation Xr in a sample of n from an exponential distribution, based on the observed values of the first k ordered observations from the sample (k < r ≤ n), is discussed. It is shown how to find an interval estimate for Xr , and the result is used to predict the remaining elapsed time in certain life test experiments involving items whose life times follow an exponential distribution.
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Jerald F. Lawless (1971) studied this question.
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