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Prediction Intervals for Future Order Statistics from Two Independent Sequences

Received: 23 December 2014     Accepted: 6 January 2015     Published: 2 February 2015
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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.

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 1)
DOI 10.11648/j.ajtas.20150401.16
Page(s) 33-40
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Distribution-Free Prediction Intervals, Order Statistics, Progressive Type-II Right Censoring, Coverage Probability

References
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[2] J. Ahmadi, N. Balakrishnan, Distribution-free confidence intervals for quantile intervals based on current records, Stat. Prob. Letters 75 (2005) 190 – 202.
[3] J. Ahmadi, N. Balakrishnan, Prediction of order statistics and record values from two independent sequences, Statistics 44 (2010) 417– 430.
[4] J. Ahmadi, N. Balakrishnan, Distribution-free prediction intervals for order statistics based on record coverage, J. Korean Stat. Society 40 (2011) 181 – 192.
[5] J. Ahmadi, N. Balakrishnan, Outer and inner prediction intervals for order statistics based on current records, Springer 53 (2012) 789– 802.
[6] J. Ahmadi, S.M.T.K. MirMostafaee, N. Balakrishnan, Nonparametric prediction intervals for future record intervals based on order statistics, Stat. Prob. Letters 80 (2010) 1663 – 1672.
[7] M.Z. Raqab, Distribution-free prediction intervals for the future current record statistics, Springer 50 (2009) 429– 439.
[8] M. Z. Raqab, N. Balakrishnan, Prediction intervals for future records, Stat. Prob. Letters, 78 (2008) 1955 – 1963.
[9] B.C. Arnold, N. Balakrishnan, H.N. Nagaraja, A First Course in Order Statistics, John Wiley - Sons, New York (1992).
[10] H.A. David, H.N. Nagaraja, Order Statistics, third ed.. John Wiley - Sons, Hoboken, New Jersey (2008).
[11] N. Balakrishnan, Progressive censoring methodology: an appraisal, Springer, 16 (2007) 211 – 259.
[12] N. Balakrishnan, A. Childs, B. Chandrasekar, An efficient computational method for moments of order statistics under progressive censoring, Stat. Prob. Letters, 60 (2002) 359 – 365.
[13] M. Z. Raqab, N. Balakrishnan, Prediction intervals for future records, Stat. Prob. Letters, 78 (2008) 1955 – 1963.
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Cite This Article
  • APA Style

    M. M. Mohie El-Din, M. S. Kotb, W. S. Emam. (2015). Prediction Intervals for Future Order Statistics from Two Independent Sequences. American Journal of Theoretical and Applied Statistics, 4(1), 33-40. https://doi.org/10.11648/j.ajtas.20150401.16

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    ACS Style

    M. M. Mohie El-Din; M. S. Kotb; W. S. Emam. Prediction Intervals for Future Order Statistics from Two Independent Sequences. Am. J. Theor. Appl. Stat. 2015, 4(1), 33-40. doi: 10.11648/j.ajtas.20150401.16

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    AMA Style

    M. M. Mohie El-Din, M. S. Kotb, W. S. Emam. Prediction Intervals for Future Order Statistics from Two Independent Sequences. Am J Theor Appl Stat. 2015;4(1):33-40. doi: 10.11648/j.ajtas.20150401.16

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  • @article{10.11648/j.ajtas.20150401.16,
      author = {M. M. Mohie El-Din and M. S. Kotb and W. S. Emam},
      title = {Prediction Intervals for Future Order Statistics from Two Independent Sequences},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {4},
      number = {1},
      pages = {33-40},
      doi = {10.11648/j.ajtas.20150401.16},
      url = {https://doi.org/10.11648/j.ajtas.20150401.16},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150401.16},
      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.},
     year = {2015}
    }
    

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    AB  - 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.
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Author Information
  • Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt

  • Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt

  • Department of Basic Science , Faculty of Engineering, British University in Egypt, Al-Shorouq City, Cairo, Egypt

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