Research Article Open Access

Prediction Intervals for Future Observations Based on Samples of Random Sizes

Mohammad Z. Raqab1 and Haroon M. Barakat2
  • 1 The University of Jordan, Jordan
  • 2 Zagazig University, Egypt

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.

Journal of Mathematics and Statistics
Volume 14 No. 1, 2018, 16-28

DOI: https://doi.org/10.3844/jmssp.2018.16.28

Submitted On: 29 September 2017 Published On: 2 January 2018

How to Cite: Raqab, M. Z. & Barakat, H. M. (2018). Prediction Intervals for Future Observations Based on Samples of Random Sizes. Journal of Mathematics and Statistics, 14(1), 16-28. https://doi.org/10.3844/jmssp.2018.16.28

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Keywords

  • Order Statistics
  • Probability Coverage
  • Random Sample Size
  • Prediction Intervals
  • Outer and Inner Intervals