IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v69y2004i4p421-430.html
   My bibliography  Save this article

Maximum variance of Kth records

Author

Listed:
  • Klimczak, Monika
  • Rychlik, Tomasz

Abstract

Papadatos (Ann. Inst. Statist. Math. 47 (1995) 185) provided sharp bounds for the variances of order statistics in population variance units. This paper presents similar results for the variances of kth record values.

Suggested Citation

  • Klimczak, Monika & Rychlik, Tomasz, 2004. "Maximum variance of Kth records," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 421-430, October.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:4:p:421-430
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00195-6
    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. Nickos Papadatos, 1995. "Maximum variance of order statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(1), pages 185-193, January.
    2. Mohammad Z. Raqab, 2000. "On the moments of record values," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 29(7), pages 1631-1647, January.
    3. Lin, G. D. & Huang, J. S., 1989. "Variances of sample medians," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 143-146, June.
    4. Bassan, Bruno & Denuit, Michel & Scarsini, Marco, 1999. "Variability orders and mean differences," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 121-130, November.
    5. Raqab, Mohammad Z., 1997. "Bounds based on greatest convex minorants for moments of record values," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 35-41, November.
    6. Danielak, Katarzyna & Raqab, Mohammad Z., 2004. "Sharp bounds on expectations of kth record spacings from restricted families," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 175-187, August.
    7. Nickos Papadatos, 1997. "A Note on Maximum Variance of Order Statistics from Symmetric Populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 117-121, March.
    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. Krzysztof Jasiński, 2018. "Relations for product moments and covariances of kth records from discrete distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 125-141, February.
    2. Rychlik, Tomasz, 2008. "Extreme variances of order statistics in dependent samples," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1577-1582, September.
    3. Jafar Ahmadi & Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2009. "Prediction of k-records from a general class of distributions under balanced type loss functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 19-33, June.

    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. Paweł Marcin Kozyra & Tomasz Rychlik, 2017. "Lower and upper bounds on the variances of spacings," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 417-428, April.
    2. Rychlik, Tomasz, 2008. "Extreme variances of order statistics in dependent samples," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1577-1582, September.
    3. Raqab, Mohammad Z., 2010. "Evaluations of the mean residual lifetime of an m-out-of-n system," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 333-342, March.
    4. Z. Raqab, Mohammad, 2003. "P-Norm bounds for moments of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 393-402, October.
    5. Marek Beśka & Krzysztof Jasiński & Tomasz Rychlik & Marcin Spryszyński, 2012. "Mixed systems with minimal and maximal lifetime variances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 877-894, October.
    6. Capaldo, Marco & Di Crescenzo, Antonio & Pellerey, Franco, 2024. "Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems," Statistics & Probability Letters, Elsevier, vol. 206(C).
    7. Jafar Ahmadi & Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2009. "Prediction of k-records from a general class of distributions under balanced type loss functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 19-33, June.
    8. Taizhong Hu & Asok K. Nanda & Huiliang Xie & Zegang Zhu, 2004. "Properties of some stochastic orders: A unified study," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(2), pages 193-216, March.
    9. Wei Jiang & Steven Kou, 2021. "Simulating risk measures via asymptotic expansions for relative errors," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 907-942, July.
    10. Jones, M.C., 2019. "Inverting Khintchine’s relationship and generating length biased data," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    11. Mariusz Bieniek, 2015. "Optimal evaluations for the bias of trimmed means of $$k$$ k th record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 437-460, May.
    12. Klimczak, Monika, 2006. "Prediction of kth records," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 117-127, January.
    13. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    14. Mariusz Bieniek & Luiza Pańczyk, 2023. "On the choice of the optimal single order statistic in quantile estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 303-333, April.
    15. Tomasz Rychlik, 2001. "Stability of Order Statistics under Dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 877-894, December.
    16. Gajek, L. & Okolewski, A., 2001. "Improved Steffensen type bounds on expectations of record statistics," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 205-212, 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:69:y:2004:i:4:p:421-430. 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.