Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 29, 2000 - Issue 8
Submit an article Journal homepage
55
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

A unified approach to binomial-type distributions of order k

Sung-il Han Department of Informatics and Mathematical Science, Osaka University, Osaka, 560-8531, JAPAN
&
Sigeo Aki Department of Informatics and Mathematical Science, Osaka University, Osaka, 560-8531, JAPAN
Pages 1929-1943 | Received 01 Oct 1999, Published online: 27 Jun 2007

References

  • Aki , S. and HiraiiG , K. 1988 . Some characteristics of the binomial distri¬bution of order k and related distributions , 211 – 222 . North-Holland : K. Matusita .
  • Aki , S. and Hirano , K. 1993 . Discrete distributions related to succession events in a two-state Markov chain , K. Matusita .
  • Aki , S. and Hirano , K. 1999 . Number of success runs of specified length until some stopping times and generalized binomial distributions of order A . Ann. Inst. Statist Math., ,
  • Chao , M. T , Fu , J. C and Koutras , M. V . 1995 . Survey of reliability stud¬ies of consecutive-£;-out-of-n:F & related systems . IEEE Transactions on Reliability , 44 : 120 – 127 .
  • Feller , W. 1968 . An Introduction to Probability Theory and Its Applications, , New York : John Wiley and Sons .
  • Godbole , A. P . 1992 . The exact and asymptotic distribution of overlapping success . Commun. Statist -Theor. Meth. , 21 : 953 – 967 .
  • Hirano , K. 1986 . Some properties of the distributions of order k , 43 – 53 . A.N. Philippou, G.E.Bergum and A.F. Horadam .
  • Hirano , K. 1994 . Consecutive-&out-of-n:F Systems . Proceedings of the Institute of Statistical Mathematics , 42 : 45 – 61 .
  • Hirano , K. and Aki , S. 1993 . On number of occurrences of success runs of specified length in a two-state Markov chain . Statistica Sinica , 3 : 313 – 320 .
  • Hirano , K. , Aki , S. , Kashiwagi , N. and Kuboki , H. 1991 . On Ling's bi¬nomial and negative binomial distributions of order fc . Statist Probab. , 3
  • Ling , K, D . 1988 . On binomial distributions of order . kn Statist Probab. Lett , 6 : 247 – 250 .
  • Philippou , A. N and Makri , F. S . 1986 . Successes, runs, and longest runs . Statist Probab. Lett , 4 : 101 – 105 .
  • Philippou , A. N , Tripsiannis , G. A and Antzoulakos , D. L . 1989 . New Polya and inverse Polya distributions of order . kn Commun. Statist. -Theor. Mem., , 18 : 2125 – 2137 .
  • Uchida , M. 1998 . On number of occurrences of success runs specified length in a higher-order two-state Markov chain . Ann. Inst Statist Math. , 50 : 587 – 601 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.