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Coxian approximations of matrix-exponential distributions
He, Qi-Ming1; Zhang, Hanqin2
Source PublicationCALCOLO
AbstractIn 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.
Keywordmatrix-exponential distribution Coxian distribution phase-type distribution matrix analytic methods Perron-Frobenius theory
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000251788800004
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Document Type期刊论文
Corresponding AuthorHe, Qi-Ming
Affiliation1.Dalhousie Univ, Dept Ind Engn, Halifax, NS B3J 2X4, Canada
2.Acad Sinica, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
He, Qi-Ming,Zhang, Hanqin. Coxian approximations of matrix-exponential distributions[J]. CALCOLO,2007,44(4):235-264.
APA He, Qi-Ming,&Zhang, Hanqin.(2007).Coxian approximations of matrix-exponential distributions.CALCOLO,44(4),235-264.
MLA He, Qi-Ming,et al."Coxian approximations of matrix-exponential distributions".CALCOLO 44.4(2007):235-264.
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