IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v79y2009i5p676-683.html
   My bibliography  Save this article

Waiting times of exceedances in random threshold models

Author

Listed:
  • Bairamov, Ismihan
  • EryIlmaz, Serkan

Abstract

Waiting time distributions associated with a sequence of binary trials have been widely studied and applied in various areas of probability and statistics. In this paper we study simple and compound waiting time random variables associated with random threshold models which make the elements of sequence dependent. The exact distributions are derived and the results are illustrated for random thresholds based on order statistics.

Suggested Citation

  • Bairamov, Ismihan & EryIlmaz, Serkan, 2009. "Waiting times of exceedances in random threshold models," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 676-683, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:5:p:676-683
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00497-5
    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. Jacek Wesołowski & Mohammad Ahsanullah, 1998. "Distributional Properties of Exceedance Statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 543-565, September.
    2. Ismihan Bairamov & Samuel Kotz, 2001. "On distributions of exceedances associated with order statistics and record values for arbitrary distributions," Statistical Papers, Springer, vol. 42(2), pages 171-185, April.
    3. S. Chakraborti & P. van der Laan & M. A. van de Wiel, 2004. "A class of distribution‐free control charts," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 443-462, August.
    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. Eryilmaz, Serkan & Gebizlioglu, Omer L. & Tank, Fatih, 2011. "Modeling of claim exceedances over random thresholds for related insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 496-500.

    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. EryIlmaz, S. & Bairamov, I. G., 2003. "On a new sample rank of an order statistics and its concomitant," Statistics & Probability Letters, Elsevier, vol. 63(2), pages 123-131, June.
    2. Eryilmaz, Serkan & Gebizlioglu, Omer L. & Tank, Fatih, 2011. "Modeling of claim exceedances over random thresholds for related insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 496-500.
    3. Willem Albers & Wilbert C. M. Kallenberg, 2009. "Normal control charts with nonparametric safeguard," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(1), pages 63-81, February.
    4. Nikolaos I. Panayiotou & Ioannis S. Triantafyllou, 2023. "A Class of Enhanced Nonparametric Control Schemes Based on Order Statistics and Runs," Stats, MDPI, vol. 6(1), pages 1-14, February.
    5. M. A. Graham & S. W. Human & S. Chakraborti, 2010. "A Phase I nonparametric Shewhart-type control chart based on the median," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1795-1813.
    6. Graham, M.A. & Mukherjee, A. & Chakraborti, S., 2012. "Distribution-free exponentially weighted moving average control charts for monitoring unknown location," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2539-2561.
    7. Erem, Aysegul & Bayramoglu, Ismihan, 2017. "Exact and asymptotic distributions of exceedance statistics for bivariate random sequences," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 181-188.
    8. Ismihan Bairamov & Samuel Kotz, 2001. "On distributions of exceedances associated with order statistics and record values for arbitrary distributions," Statistical Papers, Springer, vol. 42(2), pages 171-185, April.
    9. Sotiris Bersimis & Kostas Triantafyllopoulos, 2020. "Dynamic Non-parametric Monitoring of Air-Pollution," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1457-1479, December.
    10. Willem Albers & Wilbert Kallenberg, 2009. "CUMIN charts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 111-130, June.
    11. Agah Kozan & Burak Uyar & Halil Tanil, 2024. "Exceedance statistics based on bottom- $$k$$ k -lists," Statistical Papers, Springer, vol. 65(8), pages 5239-5251, October.
    12. EryIlmaz, Serkan, 2008. "Distribution of runs in a sequence of exchangeable multi-state trials," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1505-1513, September.
    13. Saber Ali & Zameer Abbas & Hafiz Zafar Nazir & Muhammad Riaz & Xingfa Zhang & Yuan Li, 2020. "On Designing Non-Parametric EWMA Sign Chart under Ranked Set Sampling Scheme with Application to Industrial Process," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    14. Lianjie Shu & Jinyu Fan, 2018. "A distribution‐free control chart for monitoring high‐dimensional processes based on interpoint distances," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 317-330, June.
    15. Gulder Kemalbay & Ismihan Bayramoglu (Bairamov), 2015. "Joint distribution of new sample rank of bivariate order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2280-2289, October.
    16. Nandini Das, 2011. "Control Charts Based on the g-and-h Distribution," Stochastics and Quality Control, De Gruyter, vol. 26(1), pages 3-14, January.
    17. Chakraborti, S. & Eryilmaz, S. & Human, S.W., 2009. "A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1054-1065, February.
    18. Koutras, M.V. & Sofikitou, E.M., 2017. "A new bivariate semiparametric control chart based on order statistics and concomitants," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 340-347.

    More about this item

    Statistics

    Access and download statistics

    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:79:y:2009:i:5:p:676-683. 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.