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

| Peer-Reviewed

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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

[1]	J. Ahmadi, N. Balakrishnan, Confidence intervals for quantiles in terms of record range, Stat. Prob. Letters 68 (2004) 395 – 405.
[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.
[14]	D. Krewski, Distribution-free confidence intervals for quantile intervals, J. American Stat. Association, 71 (1976) 420 – 422.
[15]	E.K. Al-Hussaini, Generalized order statistics: prospective and applications, J. Appl. Stat. Sci. 4 (2004) 1 – 12.
[16]	E. Cramer, Contributions to generalized order statistics, Habilitaionss-chrift reprint, University of Oldenburg (2003).
[17]	U. Kamps, A concept of generalized order statistics, Teubner, Stuttgart (1995).
[18]	U. Kamps, E. Cramer, On distributions of generalized order statistics, Statistics 35 (2001) 269 – 280.
[19]	J.F. Lawless, Statistical model & methods for lifetime data, Wiley, New York (1982).
[20]	W.B. Nelson, Applied life data analysis, Wiley, New York (1982).

Cite This Article

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

Copy | Download

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

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

Download PDF

Sections

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

Copy | Download

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