Volume 4, Issue 1, January 2015, Page: 33-40
Prediction Intervals for Future Order Statistics from Two Independent Sequences
M. M. Mohie El-Din, Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt
M. S. Kotb, Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt
W. S. Emam, Department of Basic Science , Faculty of Engineering, British University in Egypt, Al-Shorouq City, Cairo, Egypt
Received: Dec. 23, 2014;       Accepted: Jan. 6, 2015;       Published: Feb. 2, 2015
DOI: 10.11648/j.ajtas.20150401.16      View  2465      Downloads  133
Abstract
In this article, based on observed X-sequence of independent and identically distribution (iid) continuous random variables, we discuss the problem of predicting future order statistics from a Y-sequence of iid continuous random variables from the same distribution. Specifically, distribution-free prediction intervals (PIs) for an order statistic observation based on either progressive Type-II right censoring, or order data from the past X-sequence, as well as outer and inner PIs are derived based on order statistics observations. Such these intervals are exact and do not depend on the sampling distribution. Finally, a real life time data set that given to breakdown of an insulating fluid between electrodes is used to illustrate the proposed procedures.
Keywords
Distribution-Free Prediction Intervals, Order Statistics, Progressive Type-II Right Censoring, Coverage Probability
To cite this article
M. M. Mohie El-Din, M. S. Kotb, W. S. Emam, Prediction Intervals for Future Order Statistics from Two Independent Sequences, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 1, 2015, pp. 33-40. doi: 10.11648/j.ajtas.20150401.16
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