IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v68y2004i4p395-405.html
   My bibliography  Save this article

Confidence intervals for quantiles in terms of record range

Author

Listed:
  • Ahmadi, J.
  • Balakrishnan, N.

Abstract

Often, in industrial stress testing, meteorological data analysis, athletic events, and other similar situations, measurements may be made sequentially and only values larger or smaller than all previous ones are observed. When the number of records is fixed in advance, the data are referred to as inversely sampled record breaking data. In this paper, we introduce some properties of current records. Distribution-free confidence intervals are derived to estimate the fixed quantiles of an arbitrary unknown distribution, based on current records of an iid sequence from that distribution. Several universal upper bounds for the expectation of the length of the confidence intervals are derived. Some tables are also provided in order to choose the appropriate records. The results may be of interest in some life testing situations.

Suggested Citation

  • Ahmadi, J. & Balakrishnan, N., 2004. "Confidence intervals for quantiles in terms of record range," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 395-405, July.
  • Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:395-405
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00129-4
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. J. Ahmadi & N. Arghami, 2003. "Nonparametric confidence and tolerance intervals from record values data," Statistical Papers, Springer, vol. 44(4), pages 455-468, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmadi, J. & Razmkhah, M. & Balakrishnan, N., 2009. "Current k-records and their use in distribution-free confidence intervals," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 29-37, January.
    2. Ahmadi, Jafar & Fashandi, M., 2009. "Some characterization and ordering results based on entropies of current records," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2053-2059, October.
    3. Amini, Morteza & Balakrishnan, N., 2013. "Nonparametric meta-analysis of independent samples of records," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 70-81.
    4. Ahmadi, J. & Balakrishnan, N., 2008. "Nonparametric confidence intervals for quantile intervals and quantile differences based on record statistics," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1236-1245, August.
    5. Raqab, Mohammad Z. & Balakrishnan, N., 2008. "Prediction intervals for future records," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1955-1963, September.
    6. Mohammad Raqab, 2009. "Distribution-free prediction intervals for the future current record statistics," Statistical Papers, Springer, vol. 50(2), pages 429-439, March.
    7. Ahmadi, J. & Balakrishnan, N., 2005. "Distribution-free confidence intervals for quantile intervals based on current records," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 190-202, December.
    8. Razmkhah, M. & Ahmadi, Jafar, 2013. "Pitman closeness of current k-records to population quantiles," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 148-156.
    9. M. Emadi & J. Ahmadi & N. Arghami, 2007. "Comparison of record data and random observations based on statistical evidence," Statistical Papers, Springer, vol. 48(1), pages 1-21, January.
    10. Ahmadi, Jafar & Balakrishnan, N., 2009. "Pitman closeness of record values to population quantiles," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2037-2044, October.
    11. S. Baratpour & J. Ahmadi & N. Arghami, 2007. "Entropy properties of record statistics," Statistical Papers, Springer, vol. 48(2), pages 197-213, April.
    12. Ahmadi, Jafar & Balakrishnan, N., 2010. "Pitman closeness of current records for location-scale families," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1577-1583, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:395-405. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.