IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v50y1998i2p203-222.html
   My bibliography  Save this article

Joint Distributions of Numbers of Success-runs Until the First Consecutive k Successes in a Higher-Order Two-State Markov Chain

Author

Listed:
  • Masayuki Uchida

Abstract

No abstract is available for this item.

Suggested Citation

  • Masayuki Uchida, 1998. "Joint Distributions of Numbers of Success-runs Until the First Consecutive k Successes in a Higher-Order Two-State Markov Chain," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 203-222, June.
    • Handle: RePEc:spr:aistmt:v:50:y:1998:i:2:p:203-222
    DOI: 10.1023/A:1003489713112
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1003489713112
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1003489713112?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. Sigeo Aki & Katuomi Hirano, 1996. "Lifetime distribution and estimation problems of consecutive-k-out-of-n:F systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(1), pages 185-199, March.
    2. Ling, K. D., 1988. "On binomial distributions of order k," Statistics & Probability Letters, Elsevier, vol. 6(4), pages 247-250, March.
    3. Sigeo Aki & Katuomi Hirano, 1994. "Distributions of numbers of failures and successes until the first consecutivek successes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 193-202, March.
    4. Hirano, K. & Aki, S. & Kashiwagi, N. & Kuboki, H., 1991. "On Ling's binomial and negative binomial distributions of order k," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 503-509, June.
    5. M. Koutras, 1997. "Waiting Time Distributions Associated with Runs of Fixed Length in Two-State Markov Chains," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 123-139, 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. Antzoulakos, Demetrios L. & Boutsikas, Michael V., 2007. "A direct method to obtain the joint distribution of successes, failures and patterns in enumeration problems," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 32-39, January.

    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. Demetrios Antzoulakos & Stathis Chadjiconstantinidis, 2001. "Distributions of Numbers of Success Runs of Fixed Length in Markov Dependent Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 599-619, September.
    2. 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.
    3. 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.
    4. Frosso Makri & Zaharias Psillakis, 2013. "Exact distributions of constrained (k, ℓ) strings of failures between subsequent successes," Statistical Papers, Springer, vol. 54(3), pages 783-806, August.
    5. Sigeo Aki & Katuomi Hirano, 1995. "Joint distributions of numbers of success-runs and failures until the first consecutivek successes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 225-235, June.
    6. Han, Qing & Aki, Sigeo, 1998. "Formulae and recursions for the joint distributions of success runs of several lengths in a two-state Markov chain," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 203-214, October.
    7. Koutras, M. V. & Alexandrou, V. A., 1997. "Non-parametric randomness tests based on success runs of fixed length," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 393-404, April.
    8. Kiyoshi Inoue & Sigeo Aki, 2011. "Bivariate Fibonacci polynomials of order k with statistical applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 197-210, February.
    9. Qing Han & Sigeo Aki, 2000. "Waiting Time Problems in a Two-State Markov Chain," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 778-789, December.
    10. Frosso Makri & Zaharias Psillakis, 2011. "On runs of length exceeding a threshold: normal approximation," Statistical Papers, Springer, vol. 52(3), pages 531-551, August.
    11. Markos V. Koutras & Sotirios Bersimis & Demetrios L. Antzoulakos, 2006. "Improving the Performance of the Chi-square Control Chart via Runs Rules," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 409-426, September.
    12. 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.
    13. repec:exl:29stat:v:20:y:2019:i:3:p:1-30 is not listed on IDEAS
    14. 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.
    15. Kiyoshi Inoue, 2004. "Joint distributions associated with patterns, successes and failures in a sequence of multi-state trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 143-168, March.
    16. Ayat Al-Meanazel & Brad C. Johnson, 2020. "The Distribution of the Length of the Longest Increasing Subsequence in Random Permutations of Arbitrary Multi-sets," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1009-1021, September.
    17. M. Koutras & V. Alexandrou, 1995. "Runs, scans and URN model distributions: A unified Markov chain approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 743-766, December.
    18. Sigeo Aki, 1999. "Distributions of Runs and Consecutive Systems on Directed Trees," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 1-15, March.
    19. 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.
    20. 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.
    21. Mohammadi, Fatemeh & Saenz-de-Cabezon, Eduardo & Wynn, Henry P., 2016. "Types of signature analysis in reliability based on Hilbert series," LSE Research Online Documents on Economics 67529, London School of Economics and Political Science, LSE Library.

    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:aistmt:v:50:y:1998:i:2:p:203-222. 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.