On the modes of the negative binomial distribution of orderk
Jiguang Shao, Sheng Fu · Journal of Applied Statistics · 2016
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. mX(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) mX(2,2)=6,7,8 and mX(3,2)=16, for p=0.5; (2) mX(2,3)=13 for p=0.5. Finally, an application of negative binomial distribution of order k in continuous sampling plans is given.