The negative binomial distribution of order k and some of its properties. (English) Zbl 0566.60014

The negative binomial distribution of order k is introduced and briefly studied. First it is shown that it is a proper probability distribution. Then its probability generating function, mean and variance are derived. Finally it is shown that the number of trials until the r th k th consecutive success (r\(\geq 1, k\geq 1)\) in independent trials with constant success probability p \((0<p<1)\) is distributed as negative binomial distribution of order k. The present paper generalizes results of H. D. Shane, Fibonacci Q. 11, 517-522 (1973; Zbl 0298.60010), the author and A. A. Muwafi, ibid. 20, 28-32 (1982; Zbl 0476.60008), and the author, C. Georghiou and G. N. Philippou, Probability theory, Proc. 7th Conf., Brasov/Romania (1982).


60E05 Probability distributions: general theory
Full Text: DOI


[1] Philippou, The Fibonacci Quarterly 20 pp 28– (1982)
[2] and , 1982: A generalized geometric distribution and some of its properties. Proceedings of the 7th Conference on Probability Theor y. Brasov, Romania (to appear).
[3] Shane, The Fibonacci Quarterly 11 pp 517– (1973)
[4] Turner, The Fibonacci Quarterly 17 pp 23– (1979)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.