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	On the modes of the negative binomial distribution of order k
	Shao, Jiguang1; Fu, Sheng2
刊名	Journal of applied statistics
	2016
卷号	43期号:11页码:2131-2149
关键词	Negative binomial distribution of order k Success run Fibonacci sequence Transition probability flow graphs Probability-generating function Mode
ISSN号	0266-4763
DOI	10.1080/02664763.2015.1130802
通讯作者	Shao, jiguang(jgshao@bjtu.edu.cn)
英文摘要	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.
WOS关键词	FIBONACCI-TYPE POLYNOMIALS ; SUCCESS RUN DISTRIBUTIONS
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
语种	英语
出版者	TAYLOR & FRANCIS LTD
WOS记录号	WOS:000382570500011
内容类型	期刊论文
URI标识	http://www.corc.org.cn/handle/1471x/2375644
专题	中国科学院大学
通讯作者	Shao, Jiguang
作者单位	1.Beijing Jiaotong Univ, Dept Math, Beijing, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Shao, Jiguang,Fu, Sheng. On the modes of the negative binomial distribution of order k[J]. Journal of applied statistics,2016,43(11):2131-2149.
APA	Shao, Jiguang,&Fu, Sheng.(2016).On the modes of the negative binomial distribution of order k.Journal of applied statistics,43(11),2131-2149.
MLA	Shao, Jiguang,et al."On the modes of the negative binomial distribution of order k".Journal of applied statistics 43.11(2016):2131-2149.

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