Journal of Mathematics and Statistics

Prediction Intervals for Future Observations Based on Samples of Random Sizes

Mohammad Z. Raqab and Haroon M. Barakat

Journal of Mathematics and Statistics


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.


© 2018 Mohammad Z. Raqab and Haroon M. Barakat. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.