Generalized binomial and negative binomial distributions of orderk by thel-overlapping enumeration scheme
Author
Abstract
Suggested Citation
DOI: 10.1007/BF02530491
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- M. Koutras, 1996. "On a waiting time distribution in a sequence of Bernoulli trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 789-806, December.
- Demetrios Antzoulakos, 1999. "On Waiting Time Problems Associated with Runs in Markov Dependent Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(2), pages 323-330, June.
- Masayuki Uchida, 1998. "On Number of Occurrences of Success Runs of Specified Length in a Higher-Order Two-State Markov Chain," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 587-601, September.
- Sigeo Aki & Katuomi Hirano, 2000. "Numbers of Success-Runs of Specified Length Until Certain Stopping Time Rules and Generalized Binomial Distributions of Order k," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 767-777, December.
- 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.
- M. Chao & James Fu, 1989. "A limit theorem of certain repairable systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 809-818, December.
- 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.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Kirtee Kamalja, 2014. "On the joint distribution of success runs of several lengths in the sequence of MBT and its applications," Statistical Papers, Springer, vol. 55(4), pages 1179-1206, November.
- Spiros Dafnis & Andreas Philippou & Demetrios Antzoulakos, 2012. "Distributions of patterns of two successes separated by a string of k-2 failures," Statistical Papers, Springer, vol. 53(2), pages 323-344, May.
- 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.
- Kiyoshi Inoue & Sigeo Aki, 2018. "Joint distributions of numbers of runs of specified lengths on directed trees," Statistical Papers, Springer, vol. 59(1), pages 249-269, March.
- K. Kotwal & R. Shinde, 2006. "Joint distributions of runs in a sequence of higher-order two-state Markov trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 537-554, September.
- 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.
- Frosso Makri & Andreas Philippou, 2005. "On binomial and circular binomial distributions of orderk forl-overlapping success runs of lengthk," Statistical Papers, Springer, vol. 46(3), pages 411-432, July.
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.- R. L. Shinde & K. S. Kotwal,, 2008. "Distributions of scan statistics in a sequence of Markov Bernoulli trials," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 135-155.
- 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.
- 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.
- 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.
- 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.
- Kiyoshi Inoue & Sigeo Aki, 2018. "Joint distributions of numbers of runs of specified lengths on directed trees," Statistical Papers, Springer, vol. 59(1), pages 249-269, March.
- 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.
- 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.
- 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.
- Martin, Donald E.K., 2006. "A recursive algorithm for computing the distribution of the number of successes in higher-order Markovian trials," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 604-610, February.
- 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.
- Sigeo Aki & Katuomi Hirano, 2002. "On Waiting Time for Reversed Patterns in Random Sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 713-718, December.
- Stathis Chadjiconstantinidis & Serkan Eryilmaz, 2023. "Computing waiting time probabilities related to $$ (k_{1},k_{2},\ldots ,k_{l})$$ ( k 1 , k 2 , … , k l ) pattern," Statistical Papers, Springer, vol. 64(5), pages 1373-1390, October.
- Frosso Makri & Andreas Philippou, 2005. "On binomial and circular binomial distributions of orderk forl-overlapping success runs of lengthk," Statistical Papers, Springer, vol. 46(3), pages 411-432, July.
- 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.
- 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.
- 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.
- Cui, Lirong & Kuo, Way & Li, Jinlin & Xie, Min, 2006. "On the dual reliability systems of (n,f,k) and," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1081-1088, June.
- 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.
- Y-C Hsieh, 2003. "New reliability bounds for coherent systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(9), pages 995-1001, September.
More about this item
Keywords
Run; waiting time; binomial distribution; negative binomial distribution; Poisson distribution; double generating function; probability generating function; Markov chain; Markov chain imbedding method;All these keywords.
Statistics
Access and download statisticsCorrections
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:55:y:2003:i:1:p:153-167. 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.