Abstract
On the basis of failure times of an informative sample (X-sample) of random size M of iid continuous random variables, we consider the prediction problem of failure times of another independent future sample (Y-sample) of random size N of iid variables from the same distribution. In this paper, we derive various exact prediction intervals for future failure times from the Y -sample based on the failure times from the X-sample. Specifically, prediction intervals for individual failure times as well as outer and inner prediction intervals are derived based on X-order statistics. Prediction intervals for the increments of order statistics are also investigated. Exact expressions for the coverage probabilities of these intervals are also derived and computed numerically. A practical example on a biometric data set is used to illustrate the results developed here.
Highlights
Prediction of future order statistics is of natural interest in many practical problems
Basiri et al (2016) developed various non-parametric prediction intervals of order statistics from a future sample based on observed order statistics
Barakat et al (2016) constructed prediction intervals for future two-parameter exponential lifetimes based on a random number of generalized order statistics under a general set-up
Summary
Prediction of future order statistics is of natural interest in many practical problems. Barakat et al (2011) obtained prediction intervals for future exponential lifetimes based on random generalized order statistics. Barakat et al (2014) obtained prediction intervals of future observations for a sample of random size from a continuous distribution. Basiri et al (2016) developed various non-parametric prediction intervals of order statistics from a future sample based on observed order statistics. Barakat et al (2016) constructed prediction intervals for future two-parameter exponential lifetimes based on a random number of generalized order statistics under a general set-up. We discuss Prediction Intervals (PIs) for future order statistics, Y1:N, Y2:N,..., YN:N, from a future independent sample (Y -sample) of random size N from a continuous cdf F(x); based on informative sample (Xsample) X1:M, X2:M,...,XM:M of random size M from the same distribution.
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