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On Ling's binomial and negative binomial distributions of order k

Author

Listed:
  • Hirano, K.
  • Aki, S.
  • Kashiwagi, N.
  • Kuboki, H.

Abstract

Type II binomial distribution of order k was introduced by Ling (1988). In this article the probability function, the probability generating function and asymptotic properties of the distribution are discussed. Some properties of the corresponding negative binomial distribution of order k, which was introduced by Ling (1989) are also examined.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:11:y:1991:i:6:p:503-509
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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