IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v79y2016i6d10.1007_s00184-016-0575-y.html
   My bibliography  Save this article

On the records of multivariate random sequences

Author

Listed:
  • Ismihan Bayramoglu

    (Izmir University of Economics)

Abstract

Two types of records in multivariate sequences are considered in this paper. According to the first definition, a multivariate observation is accepted as a record if it is not dominated in at least one of the coordinates of previous record and the first observation is a record. Some basic straightforward results concerning the distributions of record times and records according to this definition are given. The development of distribution theory for these types of record and also providing examples with available analytical results still involves challenging unsolved problems. Second, we consider records of bivariate sequences according to conditionally N-ordering, introduced in Bairamov (J Multivar Anal 97:797–809, 2006). The joint distributions of record times and distributions of record values are derived. Some examples, with particular underlying distributions demonstrating the availability of obtained formulae are provided.

Suggested Citation

  • Ismihan Bayramoglu, 2016. "On the records of multivariate random sequences," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 725-747, August.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:6:d:10.1007_s00184-016-0575-y
    DOI: 10.1007/s00184-016-0575-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-016-0575-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-016-0575-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Hashorva, Enkelejd & Hüsler, Jürg, 2005. "Multiple maxima in multivariate samples," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 11-17, November.
    2. Bairamov, Ismihan, 2006. "Progressive Type II censored order statistics for multivariate observations," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 797-809, April.
    3. Gnedin, Alexander V., 1998. "Records from a multivariate normal sample," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 11-15, July.
    4. Goldie, Charles M. & Resnick, Sidney I., 1995. "Many multivariate records," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 185-216, 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. N. Balakrishnan & A. Stepanov & V. B. Nevzorov, 2020. "North-east bivariate records," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 961-976, November.

    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. Clément Dombry & Michael Falk & Maximilian Zott, 2019. "On Functional Records and Champions," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1252-1277, September.
    2. Hashorva Enkelejd, 2016. "Domination of sample maxima and related extremal dependence measures," Dependence Modeling, De Gruyter, vol. 6(1), pages 88-101, May.
    3. Hashorva, Enkelejd & Rullière, Didier, 2020. "Asymptotic domination of sample maxima," Statistics & Probability Letters, Elsevier, vol. 160(C).
    4. N. Balakrishnan & A. Stepanov & V. B. Nevzorov, 2020. "North-east bivariate records," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 961-976, November.
    5. Hashorva, Enkelejd & Hüsler, Jürg, 2005. "Multiple maxima in multivariate samples," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 11-17, November.
    6. Barakat, H.M., 2009. "Multivariate order statistics based on dependent and nonidentically distributed random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 81-90, January.
    7. Nayak, S. S. & Zalki, Madhusudhan, 2001. "Almost sure limit points of record values from two independent populations," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 181-187, January.
    8. Gnedin, Alexander V., 1998. "Records from a multivariate normal sample," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 11-15, July.
    9. Eryilmaz, Serkan, 2008. "Multivariate stress-strength reliability model and its evaluation for coherent structures," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1878-1887, October.
    10. Alexandre Berred & Alexei Stepanov, 2015. "Asymptotic properties of the number of near minimum-concomitant observations in the case of progressive type-II censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 283-294, April.
    11. Hashorva, Enkelejd & Hüsler, Jürg, 2002. "Remarks on compound Poisson approximation of Gaussian random sequences," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 1-8, March.
    12. Fischer, T. & Balakrishnan, N. & Cramer, E., 2008. "Mixture representation for order statistics from INID progressive censoring and its applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1999-2015, October.
    13. H. N. Nagaraja & Pankaj K. Choudhary & N. Matalas, 2002. "Number of Records in a Bivariate Sample with Application to Missouri River Flood Data," Methodology and Computing in Applied Probability, Springer, vol. 4(4), pages 377-391, December.
    14. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jos Mara, 2009. "Multivariate order statistics via multivariate concomitants," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 946-951, May.
    15. Gnedin, A.V.Alexander V., 2004. "Best choice from the planar Poisson process," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 317-354, June.
    16. Stoev, Stilian & Wang, Yizao, 2019. "Exchangeable random partitions from max-infinitely-divisible distributions," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 50-56.
    17. Enkelejd Hashorva & Didier Rullière, 2019. "Asymptotic Domination Of Sample Maxima," Working Papers hal-02277020, HAL.
    18. Arnold, Barry C. & Castillo, Enrique & María Sarabia, José, 2009. "On multivariate order statistics. Application to ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4555-4569, October.

    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:spr:metrik:v:79:y:2016:i:6:d:10.1007_s00184-016-0575-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.