: 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.
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.
Year 2013,
Volume: 6 Issue: 3, 110 - 115, 31.12.2013
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.
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. December 2013;6(3):110-115.
Chicago
Yalcin, Femin. “On A Generalization Of Ling’S Binomial Distribution”. Istatistik Journal of The Turkish Statistical Association 6, no. 3 (December 2013): 110-15.
EndNote
Yalcin F (December 1, 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, vol. 6, no. 3, pp. 110–115, 2013.
ISNAD
Yalcin, Femin. “On A Generalization Of Ling’S Binomial Distribution”. Istatistik Journal of The Turkish Statistical Association 6/3 (December 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, vol. 6, no. 3, 2013, pp. 110-5.
Vancouver
Yalcin F. On A Generalization Of Ling’S Binomial Distribution. IJTSA. 2013;6(3):110-5.