IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i17p1855-1860.html
   My bibliography  Save this article

Lorenz ordering of order statistics

Author

Listed:
  • Kochar, Subhash

Abstract

Let Xi:n denote the ith order statistic of a random sample of size n from a continuous distribution with cdf F. Sufficient conditions are obtained on F so that Xj:m[less-than-or-equals, slant][small star, filled]Xi:n (hence Xj:m[less-than-or-equals, slant]LorenzXi:n) for i[less-than-or-equals, slant]j and n-i[greater-or-equal, slanted]m-j.

Suggested Citation

  • Kochar, Subhash, 2006. "Lorenz ordering of order statistics," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1855-1860, November.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:17:p:1855-1860
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(06)00151-9
    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. Jongwoo Jeon & Subhash Kochar & Chul Park, 2006. "Dispersive ordering—Some applications and examples," Statistical Papers, Springer, vol. 47(2), pages 227-247, March.
    2. Kleiber, Christian, 2002. "Variability ordering of heavy-tailed distributions with applications to order statistics," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 381-388, July.
    3. Kochar, Subhash C., 1996. "Dispersive ordering of order statistics," Statistics & Probability Letters, Elsevier, vol. 27(3), pages 271-274, April.
    4. Khaledi, Baha-Eldin & Kochar, Subhash, 2000. "On dispersive ordering between order statistics in one-sample and two-sample problems," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 257-261, February.
    5. Mahesh Chandra & Nozer D. Singpurwalla, 1981. "Relationships Between Some Notions Which are Common to Reliability Theory and Economics," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 113-121, February.
    6. Arnold, Barry C. & Nagaraja, H. N., 1991. "Lorenz ordering of exponential order statistics," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 485-490, June.
    7. Wilfling, Bernd, 1996. "Lorenz ordering of power-function order statistics," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 313-319, November.
    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. Alimohammadi, Mahdi & Esna-Ashari, Maryam & Cramer, Erhard, 2021. "On dispersive and star orderings of random variables and order statistics," Statistics & Probability Letters, Elsevier, vol. 170(C).
    2. Nuria Torrado & Rosa E. Lillo & Michael P. Wiper, 2012. "Sequential Order Statistics: Ageing and Stochastic Orderings," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 579-596, September.
    3. Tommaso Lando & Lucio Bertoli-Barsotti, 2020. "Stochastic dominance relations for generalised parametric distributions obtained through composition," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 297-311, December.
    4. Subhash Kochar & Maochao Xu, 2014. "On the skewness of order statistics with applications," Annals of Operations Research, Springer, vol. 212(1), pages 127-138, January.
    5. Lando, Tommaso & Bertoli-Barsotti, Lucio, 2020. "Second-order stochastic dominance for decomposable multiparametric families with applications to order statistics," Statistics & Probability Letters, Elsevier, vol. 159(C).

    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. Kleiber, Christian, 2002. "Variability ordering of heavy-tailed distributions with applications to order statistics," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 381-388, July.
    2. Alimohammadi, Mahdi & Esna-Ashari, Maryam & Cramer, Erhard, 2021. "On dispersive and star orderings of random variables and order statistics," Statistics & Probability Letters, Elsevier, vol. 170(C).
    3. Mesfioui Mhamed & Trufin Julien, 2021. "Dispersive order comparisons on extreme order statistics from homogeneous dependent random vectors," Dependence Modeling, De Gruyter, vol. 9(1), pages 385-393, January.
    4. Jongwoo Jeon & Subhash Kochar & Chul Park, 2006. "Dispersive ordering—Some applications and examples," Statistical Papers, Springer, vol. 47(2), pages 227-247, March.
    5. Lando, Tommaso & Bertoli-Barsotti, Lucio, 2020. "Second-order stochastic dominance for decomposable multiparametric families with applications to order statistics," Statistics & Probability Letters, Elsevier, vol. 159(C).
    6. Kleiber, Christian, 2002. "Lorenz ordering of order statistics from log-logistic and related distributions," Technical Reports 2002,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Van Delft, Christian & Kerbache, Laoucine & El Khoury, Hiba, 2011. "Optimal strategy for stochastic product rollover under risk using CVAR analysis," HEC Research Papers Series 958, HEC Paris.
    8. Fernández-Ponce, J.M. & Pellerey, F. & Rodríguez-Griñolo, M.R., 2011. "A characterization of the multivariate excess wealth ordering," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 410-417.
    9. Da, Gaofeng & Xu, Maochao & Balakrishnan, N., 2014. "On the Lorenz ordering of order statistics from exponential populations and some applications," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 88-97.
    10. Gattone, Stefano Antonio & Fortuna, Francesca & Evangelista, Adelia & Di Battista, Tonio, 2022. "Simultaneous confidence bands for the functional mean of convex curves," Econometrics and Statistics, Elsevier, vol. 24(C), pages 183-193.
    11. Walter Piesch, 2005. "A look at the structure of some extended Ginis," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 263-296.
    12. Nappo, G. & Spizzichino, F., 1998. "Ordering properties of the TTT-plot of lifetimes with Schur joint densities," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 195-203, August.
    13. Trajtenberg, Manuel & Yitzhaki, Shlomo, 1989. "The Diffusion of Innovations: A Methodological Reappraisal," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(1), pages 35-47, January.
    14. Khaledi, Baha-Eldin & Kochar, Subhash, 2000. "On dispersive ordering between order statistics in one-sample and two-sample problems," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 257-261, February.
    15. Ebrahim Amini-Seresht & Jianfei Qiao & Yiying Zhang & Peng Zhao, 2016. "On the skewness of order statistics in multiple-outlier PHR models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 817-836, October.
    16. Dongchu Sun & James Berger, 1994. "Bayesian sequential reliability for Weibull and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 221-249, June.
    17. Kochar, Subhash & Xu, Maochao, 2008. "A new dependence ordering with applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2172-2184, October.
    18. Fernández-Ponce, J.M. & Rodríguez-Griñolo, R., 2006. "Preserving multivariate dispersion: An application to the Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1208-1220, May.
    19. N. Nair & P. Sankaran & S. Sunoj, 2013. "Quantile based stop-loss transform and its applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(2), pages 167-182, June.
    20. James Townsend & Hans Colonius, 2005. "Variability of the MAX and MIN Statistic: A Theory of the Quantile Spread as a Function of Sample Size," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 759-772, December.

    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:76:y:2006:i:17:p:1855-1860. 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.