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On A Generalization Of Ling’S Binomial Distribution

Yıl 2013, Cilt: 6 Sayı: 3, 110 - 115, 31.12.2013

Öz

: In a sequence of n binary trials, distribution of the random variable Mn,k, denoting the
number of overlapping success runs of length exactly k, is called Ling’s binomial distribution or Type II
binomial distribution of order k. In this paper, we generalize Ling’s binomial distribution to Ling’s q-binomial
distribution using Bernoulli trials with a geometrically varying success probability. An expression for the
probability mass function of this distribution is derived. For q = 1, this distribution reduces to Ling’s binomial
distribution. 

Kaynakça

  • Charalambides, C.A., 2010, The q-Bernstein Basis as a q-Binomial Distributions, Journal of Statistical Planning and Inference, 140, 2184-2190.
  • Godbole, A.P., 1992 The Exact and Asymptotic Distribution of Overlapping Success Runs, Communications in Statistics-Theory and Methods, 21, 953-967.
  • Hirano, K., 1986, Some Properties of the Distributions of Order k, Fibonacci Numbers and Their Applications (eds. G.E. Bergum, A.N. Philippou, and A.F. Horadam), 43-53.
  • Ling, K.D., 1988, On Binomial Distribution of Order k, Statistics & Probability Letters, 6, 247-250.
  • Makri, F. S., Philippo, A. N., and Psillakis, Z. M., 2007, Polya, Inverse Polya, and Circular Polya Distributions of Order k for l-Overlapping Success Runs, Communications in Statistics-Theory and Methods, 36, 657-668.
  • Philippou, A.N. and Makri, F.S., 1986, Success Runs and Longest Runs, Statistics & Probability Letters, 4, 211-215.
  • Yalcin, F. and Eryilmaz, S., 2014, q-Geometric and q-Binomial Distributions of Order k, Journal of Computational and Applied Mathematics, 271, 31-38.
Yıl 2013, Cilt: 6 Sayı: 3, 110 - 115, 31.12.2013

Öz

Kaynakça

  • Charalambides, C.A., 2010, The q-Bernstein Basis as a q-Binomial Distributions, Journal of Statistical Planning and Inference, 140, 2184-2190.
  • Godbole, A.P., 1992 The Exact and Asymptotic Distribution of Overlapping Success Runs, Communications in Statistics-Theory and Methods, 21, 953-967.
  • Hirano, K., 1986, Some Properties of the Distributions of Order k, Fibonacci Numbers and Their Applications (eds. G.E. Bergum, A.N. Philippou, and A.F. Horadam), 43-53.
  • Ling, K.D., 1988, On Binomial Distribution of Order k, Statistics & Probability Letters, 6, 247-250.
  • Makri, F. S., Philippo, A. N., and Psillakis, Z. M., 2007, Polya, Inverse Polya, and Circular Polya Distributions of Order k for l-Overlapping Success Runs, Communications in Statistics-Theory and Methods, 36, 657-668.
  • Philippou, A.N. and Makri, F.S., 1986, Success Runs and Longest Runs, Statistics & Probability Letters, 4, 211-215.
  • Yalcin, F. and Eryilmaz, S., 2014, q-Geometric and q-Binomial Distributions of Order k, Journal of Computational and Applied Mathematics, 271, 31-38.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Femin Yalcin Bu kişi benim 0000-0003-0602-9392

Yayımlanma Tarihi 31 Aralık 2013
Kabul Tarihi 1 Ekim 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 6 Sayı: 3

Kaynak Göster

APA Yalcin, F. (2013). On A Generalization Of Ling’S Binomial Distribution. Istatistik Journal of The Turkish Statistical Association, 6(3), 110-115.
AMA Yalcin F. On A Generalization Of Ling’S Binomial Distribution. IJTSA. Aralık 2013;6(3):110-115.
Chicago Yalcin, Femin. “On A Generalization Of Ling’S Binomial Distribution”. Istatistik Journal of The Turkish Statistical Association 6, sy. 3 (Aralık 2013): 110-15.
EndNote Yalcin F (01 Aralık 2013) On A Generalization Of Ling’S Binomial Distribution. Istatistik Journal of The Turkish Statistical Association 6 3 110–115.
IEEE F. Yalcin, “On A Generalization Of Ling’S Binomial Distribution”, IJTSA, c. 6, sy. 3, ss. 110–115, 2013.
ISNAD Yalcin, Femin. “On A Generalization Of Ling’S Binomial Distribution”. Istatistik Journal of The Turkish Statistical Association 6/3 (Aralık 2013), 110-115.
JAMA Yalcin F. On A Generalization Of Ling’S Binomial Distribution. IJTSA. 2013;6:110–115.
MLA Yalcin, Femin. “On A Generalization Of Ling’S Binomial Distribution”. Istatistik Journal of The Turkish Statistical Association, c. 6, sy. 3, 2013, ss. 110-5.
Vancouver Yalcin F. On A Generalization Of Ling’S Binomial Distribution. IJTSA. 2013;6(3):110-5.