Coxian approximations of matrix-exponential distributions
In this paper, we study the approximation of matrix-exponential distributions by Coxian distributions. Based on the spectral polynomial algorithm, we develop an algorithm for computing Coxian representations of Coxian distributions that are approximations of matrix-exponential distributions. As a sp...
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| Published in | Calcolo Vol. 44; no. 4; pp. 235 - 264 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Milano
Springer Nature B.V
01.12.2007
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0008-0624 1126-5434 |
| DOI | 10.1007/s10092-007-0139-7 |
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| Abstract | In this paper, we study the approximation of matrix-exponential distributions by Coxian distributions. Based on the spectral polynomial algorithm, we develop an algorithm for computing Coxian representations of Coxian distributions that are approximations of matrix-exponential distributions. As a specialization, we show that phase-type (PH) distributions can be approximated by Coxian distributions. We also show that any phase-type generator with only real eigenvalues is PH-majorized by ordered Coxian generators. Consequently, the algorithm is modified for computing ordered Coxian representations of any phase-type distribution whose Laplace-Stieltjes transform has only real poles. Numerical examples are presented to show the efficiency of the algorithm and the accuracy of the Coxian approximations. Keywords: Matrix-exponential distribution, Coxian distribution, phase-type distribution, matrix analytic methods, Perron-Frobenius theory Mathematics subject classification (2000): Primary 60A99, Secondary 15A18 [PUBLICATION ABSTRACT] |
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| AbstractList | In this paper, we study the approximation of matrix-exponential distributions by Coxian distributions. Based on the spectral polynomial algorithm, we develop an algorithm for computing Coxian representations of Coxian distributions that are approximations of matrix-exponential distributions. As a specialization, we show that phase-type (PH) distributions can be approximated by Coxian distributions. We also show that any phase-type generator with only real eigenvalues is PH-majorized by ordered Coxian generators. Consequently, the algorithm is modified for computing ordered Coxian representations of any phase-type distribution whose Laplace-Stieltjes transform has only real poles. Numerical examples are presented to show the efficiency of the algorithm and the accuracy of the Coxian approximations.Keywords: Matrix-exponential distribution, Coxian distribution, phase-type distribution, matrix analytic methods, Perron-Frobenius theoryMathematics subject classification (2000): Primary 60A99, Secondary 15A18 In this paper, we study the approximation of matrix-exponential distributions by Coxian distributions. Based on the spectral polynomial algorithm, we develop an algorithm for computing Coxian representations of Coxian distributions that are approximations of matrix-exponential distributions. As a specialization, we show that phase-type (PH) distributions can be approximated by Coxian distributions. We also show that any phase-type generator with only real eigenvalues is PH-majorized by ordered Coxian generators. Consequently, the algorithm is modified for computing ordered Coxian representations of any phase-type distribution whose Laplace-Stieltjes transform has only real poles. Numerical examples are presented to show the efficiency of the algorithm and the accuracy of the Coxian approximations. Keywords: Matrix-exponential distribution, Coxian distribution, phase-type distribution, matrix analytic methods, Perron-Frobenius theory Mathematics subject classification (2000): Primary 60A99, Secondary 15A18 [PUBLICATION ABSTRACT] |
| Author | Zhang, Hanqin He, Qi-Ming |
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| CitedBy_id | crossref_primary_10_1080_17513758_2021_1912418 crossref_primary_10_1016_j_ijepes_2017_03_006 crossref_primary_10_1109_TR_2015_2494374 crossref_primary_10_1287_ijoc_1100_0383 crossref_primary_10_4236_ojop_2015_43008 crossref_primary_10_1080_15326349_2014_1003271 crossref_primary_10_1007_s40092_018_0299_x |
| Cites_doi | 10.1016/0026-2714(82)90033-6 10.1080/15326349908807560 10.1016/S0166-5316(03)00044-0 10.1201/b17050-17 10.1137/1.9780898719734 10.1080/07408178508975280 10.1016/B978-0-12-092250-5.50009-6 10.1081/STM-200056231 10.1142/9789812779311 10.1080/0020717031000114986 |
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