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On the modes of the negative binomial distribution of order k

Author:
Shao, Jiguang  Fu, Sheng  


Journal:
JOURNAL OF APPLIED STATISTICS


Issue Date:
2016


Abstract(summary):

In this paper, the modes of the negative binomial distribution of order k are studied. Firstly, the method of transition probability flow graphs is introduced to deal with the probability-generating function of the geometric distribution of order k, which is a special case of the negative binomial distribution of the same order. And then, the general negative binomial distribution of order k is investigated. By means of probability distribution function, the mode of the geometric distribution of order k is derived, i.e. m(X(k)) = k. Based on the Fibonacci sequence and Poly-nacci sequence, the modes of the negative binomial distribution of order k in some cases are obtained: (1) m(X(2,2)) = 6, 7, 8 and m(X(3,2)) = 16, for p = 0.5; (2) m(X(2,3)) = 13 for p = 0.5. Finally, an application of negative binomial distribution of order k in continuous sampling plans is given.


Page:
2131---2149


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