IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v52y2011i3p531-551.html
   My bibliography  Save this article

On runs of length exceeding a threshold: normal approximation

Author

Listed:
  • Frosso Makri
  • Zaharias Psillakis

Abstract

No abstract is available for this item.

Suggested Citation

  • Frosso Makri & Zaharias Psillakis, 2011. "On runs of length exceeding a threshold: normal approximation," Statistical Papers, Springer, vol. 52(3), pages 531-551, August.
    • Handle: RePEc:spr:stpapr:v:52:y:2011:i:3:p:531-551
    DOI: 10.1007/s00362-009-0268-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-009-0268-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-009-0268-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. Binswanger, K. & Embrechts, P., 1994. "Longest runs in coin tossing," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 139-149, December.
    2. James Fu & W. Lou & Zhi-Dong Bai & Gang Li, 2002. "The Exact and Limiting Distributions for the Number of Successes in Success Runs Within a Sequence of Markov-Dependent Two-State Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 719-730, December.
    3. D. Antzoulakos & S. Bersimis & M. Koutras, 2003. "On the distribution of the total number of run lengths," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 865-884, December.
    4. Ling, K. D., 1988. "On binomial distributions of order k," Statistics & Probability Letters, Elsevier, vol. 6(4), pages 247-250, March.
    5. Boutsikas, M. V. & Koutras, M. V., 2002. "Modeling claim exceedances over thresholds," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 67-83, February.
    6. Donald E. K. Martin, 2005. "Distribution of the Number of Successes in Success Runs of Length at Least k in Higher-Order Markovian Sequences," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 543-554, December.
    7. Lou, W. Y. Wendy, 2003. "The exact distribution of the k-tuple statistic for sequence homology," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 51-59, January.
    8. Serkan Eryilmaz, 2005. "On the distribution and expectation of success runs in nonhomogeneous Markov dependent trials," Statistical Papers, Springer, vol. 46(1), pages 117-128, January.
    9. Eryilmaz, Serkan, 2007. "Extension of runs to the continuous-valued sequences," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 383-388, February.
    10. Muselli, Marco, 2000. "Useful inequalities for the longest run distribution," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 239-249, February.
    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. Arapis, Anastasios N. & Makri, Frosso S. & Psillakis, Zaharias M., 2016. "On the length and the position of the minimum sequence containing all runs of ones in a Markovian binary sequence," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 45-54.
    2. Eryilmaz, Serkan, 2018. "On success runs in a sequence of dependent trials with a change point," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 91-98.
    3. Eryilmaz, Serkan, 2015. "Discrete time shock models involving runs," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 93-100.
    4. Makri, Frosso S. & Psillakis, Zaharias M. & Arapis, Anastasios N., 2015. "Length of the minimum sequence containing repeats of success runs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 28-37.

    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. Spiros D. Dafnis & Frosso S. Makri, 2022. "Weak runs in sequences of binary trials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 573-603, July.
    2. Frosso S. Makri & Zaharias M. Psillakis, 2011. "On Success Runs of Length Exceeded a Threshold," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 269-305, June.
    3. Spiros D. Dafnis & Frosso S. Makri & Markos V. Koutras, 2021. "Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 165-185, March.
    4. Serkan Eryilmaz, 2018. "Stochastic Ordering Among Success Runs Statistics in a Sequence of Exchangeable Binary Trials," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 563-573, June.
    5. Anastasios N. Arapis & Frosso S. Makri & Zaharias M. Psillakis, 2017. "Joint distribution of k-tuple statistics in zero-one sequences of Markov-dependent trials," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-13, December.
    6. Spiros D. Dafnis & Frosso S. Makri, 2023. "Distributions Related to Weak Runs With a Minimum and a Maximum Number of Successes: A Unified Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-24, March.
    7. Donald E. K. Martin, 2005. "Distribution of the Number of Successes in Success Runs of Length at Least k in Higher-Order Markovian Sequences," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 543-554, December.
    8. Stepanov, A., 2011. "Limit theorems for runs based on 'small spacings'," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 54-61, January.
    9. Sotirios Bersimis & Athanasios Sachlas & Pantelis G. Bagos, 2017. "Discriminating membrane proteins using the joint distribution of length sums of success and failure runs," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(2), pages 251-272, June.
    10. Narayanaswamy Balakrishnan & Alexei Stepanov, 2013. "Runs Based on Records: Their Distributional Properties and an Application to Testing for Dispersive Ordering," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 583-594, September.
    11. Donald E. K. Martin & Laurent Noé, 2017. "Faster exact distributions of pattern statistics through sequential elimination of states," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 231-248, February.
    12. Boutsikas V. Michael & Vaggelatou Eutichia, 2020. "On the Distribution of the Number of Success Runs in a Continuous Time Markov Chain," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 969-993, September.
    13. Markos V. Koutras & Demetrios P. Lyberopoulos, 2018. "Asymptotic results for jump probabilities associated to the multiple scan statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 951-968, October.
    14. Koutras, Vasileios M. & Koutras, Markos V. & Yalcin, Femin, 2016. "A simple compound scan statistic useful for modeling insurance and risk management problems," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 202-209.
    15. Sáenz-de-Cabezón, Eduardo & Wynn, Henry P., 2011. "Computational algebraic algorithms for the reliability of generalized k-out-of-n and related systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(1), pages 68-78.
    16. Shinde, R.L. & Kotwal, K.S., 2006. "On the joint distribution of runs in the sequence of Markov-dependent multi-state trials," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1065-1074, May.
    17. repec:exl:29stat:v:20:y:2019:i:3:p:1-30 is not listed on IDEAS
    18. Sonali Bhattacharya, 2018. "Some Identities based on Success Runs of at Least Length k," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 4(2), pages 39-43, January.
    19. Kiyoshi Inoue & Sigeo Aki, 2013. "Distributions of numbers of runs and scans on directed acyclic graphs with generation," Computational Statistics, Springer, vol. 28(3), pages 1133-1150, June.
    20. Eryilmaz, Serkan & Fu, James C., 2008. "Runs in continuous-valued sequences," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 759-765, April.
    21. Frosso S. Makri & Zaharias M. Psillakis, 2016. "On runs of ones defined on a q-sequence of binary trials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 579-602, July.

    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:stpapr:v:52:y:2011:i:3:p:531-551. 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.