Prediction Intervals for Future Order Statistics from Two Independent Sequences

M. M. Mohie El-Din; M. S. Kotb; W. S. Emam

doi:doi:10.11648/j.ajtas.20150401.16

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Prediction Intervals for Future Order Statistics from Two Independent Sequences

M. M. Mohie El-Din, M. S. Kotb, W. S. Emam

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 1)

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), 2024. Published by Science Publishing Group

Keywords

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

References

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[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.
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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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TY  - JOUR
T1  - Prediction Intervals for Future Order Statistics from Two Independent Sequences
AU  - M. M. Mohie El-Din
AU  - M. S. Kotb
AU  - W. S. Emam
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PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150401.16
DO  - 10.11648/j.ajtas.20150401.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 33
EP  - 40
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150401.16
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.
VL  - 4
IS  - 1
ER  -

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Author Information

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

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Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Prediction Intervals for Future Order Statistics from Two Independent Sequences
AU  - M. M. Mohie El-Din
AU  - M. S. Kotb
AU  - W. S. Emam
Y1  - 2015/02/02
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150401.16
DO  - 10.11648/j.ajtas.20150401.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 33
EP  - 40
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150401.16
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.
VL  - 4
IS  - 1
ER  -

Copy | Download