## 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).

### MSC:

 6e+06 Probability distributions: general theory

### Citations:

Zbl 0298.60010; Zbl 0476.60008
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### References:

 [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)
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