Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences

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

doi:doi:10.11648/j.ajtas.20150405.13

| Peer-Reviewed

Prediction Intervals for Progressive Type-II Right-Censored 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 5)

Received: 18 March 2015 Accepted: 29 March 2015 Published: 3 August 2015

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This article discusses the problem of predicting future progressive Type-II right censored order statistics based on progressive Type-II right-censored, ordered statistics, record values and current records that observed from the past X-sequence. Such coverage probabilities of the prediction intervals are exact and don’t depend on the sampling distribution F. Finally, a real life time data were given to breakdown the insulating fluid between electrodes which is used to illustrate the derived results.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 5)
DOI	10.11648/j.ajtas.20150405.13
Page(s)	329-338
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

Prediction Intervals, Progressive Censoring, Order Statistics, Records, Coverage Probability, Prediction Coefficient

References

[1]	D. Krewski, Distribution-free confidence intervals for quantile intervals, J. American Stat. Association, 71 (1976) 420 – 422.
[2]	J. Ahmadi, N. Balakrishnan, Confidence intervals for quantiles in terms of record range, Stat. Prob. Letters 68 (2004) 395 – 405.
[3]	J. Ahmadi, N. Balakrishnan, Distribution-free confidence intervals for quantile intervals based on current records, Stat. Prob. Letters 75 (2005) 190 – 202.
[4]	J. Ahmadi, N. Balakrishnan, outer and inner prediction intervals for order statistics based on current records, Springer, 53 (2012) 789– 802.
[5]	M. Z. Raqab, N. Balakrishnan, Prediction intervals for future records, Stat. Prob. Letters, 78 (2008) 1955 – 1963.
[6]	J. Ahmadi, N. Balakrishnan, Prediction of order statistics and record values from two independent sequences, Statistics, 44 (2010) 417– 430.
[7]	J. Ahmadi, N. Balakrishnan, Distribution-free prediction intervals for order statistics based on record coverage, J. Korean Stat. Society, 40 (2011) 181 – 192.
[8]	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.
[9]	M.Z. Raqab, Distribution-free prediction intervals for the future current record statistics, Springer, 50 (2009) 429– 439.
[10]	M. Z. Raqab, N. Balakrishnan, Prediction intervals for future records, Stat. Prob. Letters, 78 (2008) 1955 – 1963.
[11]	M. M. Mohie El-Din, M. S. Kotb, W. S. Emam, Prediction intervals for future order statistics from two independent sequences, AJTAS, 4 (2015) 33 – 40.
[12]	U. Kamps, E. Cramer, On distributions of generalized order statistics, Statistics, 35 (2001) 269 – 280.
[13]	E. Basiri, M. Z. Raqab, Nonparametric prediction intervals for progressive Type-II censored order statistics based on k-records, Springer, 28 (2013) 2825 – 2848.
[14]	R. Aggarwala, N. Balakrishnan, Progressive censoring: theory,methods, and applications. Birkhäuser, Boston (2000).
[15]	N. Balakrishnan, Progressive censoring methodology: an appraisal, Springer, 16 (2007) 211 – 259.
[16]	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.
[17]	B.C. Arnold, N. Balakrishnan, H.N. Nagaraja, A First Course in Order Statistics, John Wiley - Sons, New York, (1992).
[18]	V.B. Nevzorov, Records, Mathematical Theory (English Translation), American Mathematical Society, Providence,, (2000).
[19]	S. Gulati, W.J. Padgett, Parametric and Nonparametric Inference from Record-Breaking Data,Springer-Verlag, New York, (2003).
[20]	M. Ahsanullah, Record Values — Theory and Applications, University Press of America Inc., New York, (2004).
[21]	B.C. Arnold, N. Balakrishnan, H.N. Nagaraja, Records, John Wiley - Sons, New York, (1998).
[22]	W.B. Nelson, Applied life data analysis, Wiley, New York, (1982).
[23]	J.F. Lawless, Statistical model & methods for lifetime data, Wiley, New York, (1982).
[24]	H.A. David, H.N. Nagaraja, Order Statistics, third ed. John Wiley - Sons, Hoboken, New Jersey, (2008).

Cite This Article

Plain Text BibTeX RIS

APA Style

M. M. Mohie El-Din, M. S. Kotb, W. S. Emam. (2015). Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences. American Journal of Theoretical and Applied Statistics, 4(5), 329-338. https://doi.org/10.11648/j.ajtas.20150405.13

Copy | Download

ACS Style

M. M. Mohie El-Din; M. S. Kotb; W. S. Emam. Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences. Am. J. Theor. Appl. Stat. 2015, 4(5), 329-338. doi: 10.11648/j.ajtas.20150405.13

Copy | Download

AMA Style

M. M. Mohie El-Din, M. S. Kotb, W. S. Emam. Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences. Am J Theor Appl Stat. 2015;4(5):329-338. doi: 10.11648/j.ajtas.20150405.13

Copy | Download

@article{10.11648/j.ajtas.20150405.13,
  author = {M. M. Mohie El-Din and M. S. Kotb and W. S. Emam},
  title = {Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {5},
  pages = {329-338},
  doi = {10.11648/j.ajtas.20150405.13},
  url = {https://doi.org/10.11648/j.ajtas.20150405.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150405.13},
  abstract = {This article discusses the problem of predicting future progressive Type-II right censored order statistics based on progressive Type-II right-censored, ordered statistics, record values and current records that observed from the past X-sequence. Such coverage probabilities of the prediction intervals are exact and don’t depend on the sampling distribution F. Finally, a real life time data were given to breakdown the insulating fluid between electrodes which is used to illustrate the derived results.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences
AU  - M. M. Mohie El-Din
AU  - M. S. Kotb
AU  - W. S. Emam
Y1  - 2015/08/03
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150405.13
DO  - 10.11648/j.ajtas.20150405.13
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  - 329
EP  - 338
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150405.13
AB  - This article discusses the problem of predicting future progressive Type-II right censored order statistics based on progressive Type-II right-censored, ordered statistics, record values and current records that observed from the past X-sequence. Such coverage probabilities of the prediction intervals are exact and don’t depend on the sampling distribution F. Finally, a real life time data were given to breakdown the insulating fluid between electrodes which is used to illustrate the derived results.
VL  - 4
IS  - 5
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 Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences. American Journal of Theoretical and Applied Statistics, 4(5), 329-338. https://doi.org/10.11648/j.ajtas.20150405.13

Copy | Download

ACS Style

M. M. Mohie El-Din; M. S. Kotb; W. S. Emam. Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences. Am. J. Theor. Appl. Stat. 2015, 4(5), 329-338. doi: 10.11648/j.ajtas.20150405.13

Copy | Download

AMA Style

M. M. Mohie El-Din, M. S. Kotb, W. S. Emam. Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences. Am J Theor Appl Stat. 2015;4(5):329-338. doi: 10.11648/j.ajtas.20150405.13

Copy | Download

@article{10.11648/j.ajtas.20150405.13,
  author = {M. M. Mohie El-Din and M. S. Kotb and W. S. Emam},
  title = {Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {5},
  pages = {329-338},
  doi = {10.11648/j.ajtas.20150405.13},
  url = {https://doi.org/10.11648/j.ajtas.20150405.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150405.13},
  abstract = {This article discusses the problem of predicting future progressive Type-II right censored order statistics based on progressive Type-II right-censored, ordered statistics, record values and current records that observed from the past X-sequence. Such coverage probabilities of the prediction intervals are exact and don’t depend on the sampling distribution F. Finally, a real life time data were given to breakdown the insulating fluid between electrodes which is used to illustrate the derived results.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Prediction Intervals for Progressive Type-II Right-Censored Order Statistics from Two Independent Sequences
AU  - M. M. Mohie El-Din
AU  - M. S. Kotb
AU  - W. S. Emam
Y1  - 2015/08/03
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150405.13
DO  - 10.11648/j.ajtas.20150405.13
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  - 329
EP  - 338
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150405.13
AB  - This article discusses the problem of predicting future progressive Type-II right censored order statistics based on progressive Type-II right-censored, ordered statistics, record values and current records that observed from the past X-sequence. Such coverage probabilities of the prediction intervals are exact and don’t depend on the sampling distribution F. Finally, a real life time data were given to breakdown the insulating fluid between electrodes which is used to illustrate the derived results.
VL  - 4
IS  - 5
ER  -

Copy | Download