IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i21-22p1577-1583.html
   My bibliography  Save this article

Pitman closeness of current records for location-scale families

Author

Listed:
  • Ahmadi, Jafar
  • Balakrishnan, N.

Abstract

In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. These statistics are referred to as current upper and lower records, respectively, in the statistical literature. We derive expressions for the Pitman closeness of current records to a common population parameter and then apply these results to location-scale families of distributions with a special emphasis on the estimation of quantiles. In the case of symmetric distributions, we show that this criterion possesses some symmetry properties. Exact expressions are derived for the Pitman closeness probabilities in the case of Uniform (-1, 1) and exponential distributions. Moreover, for the population median, we show that the Pitman closeness probability is distribution-free.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:21-22:p:1577-1583
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00171-9
    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. 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.
    2. Ahmadi, Jafar & Balakrishnan, N., 2009. "Pitman closeness of record values to population quantiles," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2037-2044, October.
    3. Balakrishnan, N. & Iliopoulos, G. & Keating, J.P. & Mason, R.L., 2009. "Pitman closeness of sample median to population median," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1759-1766, August.
    4. 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.
    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. Elham Mirfarah & Jafar Ahmadi, 2014. "Pitman closeness of $$k$$ k -records from two sequences to progressive Type-II censored order statistics," Computational Statistics, Springer, vol. 29(5), pages 1279-1300, October.
    2. Razmkhah, M. & Ahmadi, Jafar, 2013. "Pitman closeness of current k-records to population quantiles," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 148-156.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Razmkhah, M. & Ahmadi, Jafar, 2013. "Pitman closeness of current k-records to population quantiles," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 148-156.
    2. 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.
    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. Raqab, Mohammad Z. & Balakrishnan, N., 2008. "Prediction intervals for future records," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1955-1963, September.
    5. 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.
    6. Ahmadi, Jafar & Balakrishnan, N., 2009. "Pitman closeness of record values to population quantiles," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2037-2044, October.
    7. Jazaa S. Al-Mutairi & Mohammad Z. Raqab, 2020. "Confidence intervals for quantiles based on samples of random sizes," Statistical Papers, Springer, vol. 61(1), pages 261-277, February.
    8. Balakrishnan, N. & Davies, Katherine F., 2013. "Pitman closeness results for Type-I censored data from exponential distribution," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2693-2698.
    9. Behboodian, J. & Bansal, Naveen & Hamedani, G.G. & Volkmer, Hans, 2013. "The Pitman inequality for exchangeable random vectors," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1825-1829.
    10. Mohammad Raqab, 2009. "Distribution-free prediction intervals for the future current record statistics," Statistical Papers, Springer, vol. 50(2), pages 429-439, March.
    11. 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.
    12. Morteza Amini & Narayanaswamy Balakrishnan, 2015. "Pooled parametric inference for minimal repair systems," Computational Statistics, Springer, vol. 30(2), pages 605-623, June.
    13. Ahmadi, Jafar & MirMostafaee, S.M.T.K. & Balakrishnan, N., 2010. "Nonparametric prediction intervals for future record intervals based on order statistics," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1663-1672, November.
    14. Jafar Ahmadi & N. Balakrishnan, 2012. "Outer and inner prediction intervals for order statistics intervals based on current records," Statistical Papers, Springer, vol. 53(3), pages 789-802, August.
    15. Jafar Ahmadi & N. Balakrishnan, 2013. "On the nearness of record values to order statistics from Pitman’s measure of closeness," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 521-541, May.
    16. Balakrishnan, N. & Davies, K.F. & Keating, J.P. & Mason, R.L., 2012. "Computation of optimal plotting points based on Pitman closeness with an application to goodness-of-fit for location-scale families," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2637-2649.
    17. 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.
    18. 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.
    19. S. MirMostafaee & Jafar Ahmadi & Narjes Sadeghian, 2015. "Pitman closeness of predictors of future order statistics for two parameter exponential distribution," Computational Statistics, Springer, vol. 30(4), pages 1163-1183, December.
    20. S. Baratpour & J. Ahmadi & N. Arghami, 2007. "Entropy properties of record statistics," Statistical Papers, Springer, vol. 48(2), pages 197-213, April.

    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:80:y:2010:i:21-22:p:1577-1583. See general information about how to correct material in RePEc.

    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 bibliographic 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.

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

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.