KMS Of Academy of mathematics and systems sciences, CAS
| THE ALGEBRAIC DEGREE OF PHASE-TYPE DISTRIBUTIONS | |
Fackrell, Mark1; He, Qi-Ming2; Taylor, Peter1; Zhang, Hanqin3
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| 2010-09-01 | |
| Source Publication | JOURNAL OF APPLIED PROBABILITY
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| ISSN | 0021-9002 |
| Volume | 47Issue:3Pages:611-629 |
| Abstract | 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. |
| Keyword | Phase-type distribution rational Laplace-Stieltjes transform algebraic degree matrix-analytic method |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Statistics & Probability |
| WOS ID | WOS:000282856000001 |
| Publisher | APPLIED PROBABILITY TRUST |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/10635 |
| Collection | 应用数学研究所 |
| Corresponding Author | Fackrell, Mark |
| Affiliation | 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 |
| Recommended Citation 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. |
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