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Dergiler / Istatistik Journal of The Turkish Statistical Association / 2026 / Volume: 9 Issue: 2

ON THE NUMBER OF l-OVERLAPPING SUCCESS RUNS OF LENGTH k UNDER q- SEQUENCE OF BINARY TRIALS

İsmail Kinaci
Coşkun Kuş
Kadir Karakaya
Yunus Akdoğan
Sayfa
—
Yayın Tarihi
2016-06-01
DOI
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The new distribution generalizes, Type I and Type IIq-binomial distributions which were recently studied in the literature

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The probability mass function, first and second moments of the number of l-overlapping successruns of length k in X1, X2, . . . , Xnare obtained.
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Temel Bulgular & Veri:The probability mass function, first and second moments of the number of l-overlapping successruns of length k in X1, X2, . . . , Xnare obtained.
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Sonuç & Katkı:The new distribution generalizes, Type I and Type IIq-binomial distributions which were recently studied in the literature
🔬Tür:Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Discrete distributions · q-Distributions · Runs

Abstract

probability. The probability mass function, first and second moments of the number of l-overlapping successruns of length k in X1, X2, . . . , Xnare obtained. The new distribution generalizes, Type I and Type IIq-binomial distributions which were recently studied in the literature

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Bu Makaleye Atıf Yap

Kinaci, İ., Kuş, C., Karakaya, K., Akdoğan, Y. (2016). ON THE NUMBER OF l-OVERLAPPING SUCCESS RUNS OF LENGTH k UNDER q- SEQUENCE OF BINARY TRIALS. Istatistik Journal of The Turkish Statistical Association, Volume: 9 Issue: 2. https://ajindex.com/articles/1636492

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Kaynakça (17)

  1. Hirano, K. (1986). Some Properties of the Distributions of Order k. Fibonacci Numbers and Their Appli- cations (eds. G.E. Bergum, A.N. Philippou, and A.F. Horadam), 43-53.
  2. Philippou, A.N. and Makri, F.S. (1986). Success Runs and Longest Runs. Statistics & Probability Letters,, 211-215.
  3. Ling, K.D. (1988). On Binomial Distribution of Order k. Statistics & Probability Letters, 6, 247-250.
  4. Makri, F.S. and Philippou, A.N. (2005). On Binomial and Circular Binomial Distributions of order k for l -overlapping success runs of length k. Statistical Papers, 46(3), 411-432.
  5. Eryilmaz, S. and Demir, S. (2007). Success runs in a sequence of exchangeable binary trials. Journal of
  6. Statistical Planning and Inference, 137, 2954–2963.
  7. Demir, S. and Eryilmaz, S. (2010). Run statistics in a sequence of arbitrarily dependent binary trials.
  8. Statistical Papers, 51, 959–973. Eryilmaz, S. and Yalcin, F. (2011). Distribution of run statistics in partially exchangeable processes. Metrika, 73, 293–304.
  9. Charalambides, C.A. (2010). The q -Bernstein basis as a q -binomial distributions. Journal of Statistical
  10. Planning and Inference, 140, 2184–2190.
  11. Yalcin, F. and Eryilmaz S. (2014). q -Geometric and q -Binomial Distributions of Order k. Journal of
  12. Computational and Applied Mathematics, 271, 31–38. Yalcin, F. (2013). On a Generalization of Ling’s Binomial Distribution. ISTATISTIK, Journal of the Turkish Statistical Association, 6(3), 110–115.
  13. Table 1. Probability mass function of N12,3,2 q x q = 0.5, θ = 0.5 q = 0.5, θ = 0.8 q = 0.8, θ = 0.5 4526 1169 0888 0694 0550 0438 0350 0312 0215 0172 0687 0002 7668 1243 0570 0270 0130 0062 0030 0016 0004 0003 0002
  14. Table 2. E Nn,k,l for different values of θ, q, n, k and l q n l k (θ, q) (0.2, 0.5) (0.5, 0.2) (0.5, 0.5) (0.5, 1) 05509 00948 00177 00034 00041 (0.8, 0.5) 64504 10233 85677 54280 97420 5 05860 05968 12499 0 2 05510 00948 00177 00034 00041 06153 06279 18749 21949 5 0 2 05510 00948 00177 00034 00041 06226 06357 24999 37657 5
  15. Table 3. V ar Nn,k,l for different values of θ, q, n, k and l q n l k (θ, q) (0.2, 0.5) (0.5, 0.2) (0.5, 0.5) (0.5, 1) 07342 01035 00191 00037 00061 (0.8, 0.5) 26448 42630 32089 66825 39907 5 14111 14252 24268 0 2 08553 01090 00192 00037 00061 16908 17082 40429 25853 5 0 2 09760 01145 00195 00037 00061 17900 18093 59765 00807 5 2 4 6 8 10 2 4 6 8 10 (n=12, l=2, q=0.5, θ=0.5) q=0.5 2 4 6 8 10 2 4 6 8 10 (n=12,k=5,q=0.5,θ=0.5) θ=0.8 2 4 6 8 10 2 4 6 8 10 (n=12, k=3, l=2, θ=0.5) 2 4 6 8 10 2 4 6 8 1012 (n=12, k=3, l=2, q=0.5)
  16. Figure 1. Probability mass function of N12,k,l for different settings 2 4 6 8 θ q=0.5, k=4 2 4 6 8 θ q=0.5, k=6 2 4 6 8 θ q=0.5, k=8 2 4 6 8 θ q=0.9, k=4 2 4 6 8 θ q=0.9, k=6 2 4 6 8 θ q=0.9, k=8 2 4 6 8 θ 2 4 6 8 θ 2 4 6 8 θ Figure 2. E N10,k,l for different values of θ, q, k and l q 2 4 6 8 θ q=0.5, k=8 2 4 6 8 θ q=0.9, k=4 2 4 6 8 θ q=0.9, k=6 2 4 6 8 θ q=0.9, k=8 2 4 6 8 θ 2 4 6 8 θ 2 4 6 8 θ Figure 3. V ar N10,k,l for different values of θ, q, k and l q
  17. Philippou, A.N. and Makri, F.S. (1986). Success Runs and Longest Runs. Statistics & Probability Letters,, 211-215.