THE ALGEBRAIC DEGREE OF PHASE-TYPE DISTRIBUTIONS

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	THE ALGEBRAIC DEGREE OF PHASE-TYPE DISTRIBUTIONS
	Fackrell, Mark 1; He, Qi-Ming 2; Taylor, Peter 1; Zhang, Hanqin3
	2010-09-01
发表期刊	JOURNAL OF APPLIED PROBABILITY
ISSN	0021-9002
卷号	47 期号:3 页码:611-629
摘要	This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator? how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.
关键词	Phase-type distribution rational Laplace-Stieltjes transform algebraic degree matrix-analytic method
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000282856000001
出版者	APPLIED PROBABILITY TRUST
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10635
专题	应用数学研究所
通讯作者	Fackrell, Mark
作者单位	1.Univ Melbourne, Dept Math & Stat, Melbourne, Vic 3010, Australia 2.Dalhousie Univ, Halifax, NS B3H 3J5, Canada 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Fackrell, Mark,He, Qi-Ming,Taylor, Peter,et al. THE ALGEBRAIC DEGREE OF PHASE-TYPE DISTRIBUTIONS[J]. JOURNAL OF APPLIED PROBABILITY,2010,47(3):611-629.
APA	Fackrell, Mark,He, Qi-Ming,Taylor, Peter,&Zhang, Hanqin.(2010).THE ALGEBRAIC DEGREE OF PHASE-TYPE DISTRIBUTIONS.JOURNAL OF APPLIED PROBABILITY,47(3),611-629.
MLA	Fackrell, Mark,et al."THE ALGEBRAIC DEGREE OF PHASE-TYPE DISTRIBUTIONS".JOURNAL OF APPLIED PROBABILITY 47.3(2010):611-629.