Coxian approximations of matrix-exponential distributions

• Published in: Calcolo Vol. 44; no. 4; pp. 235 - 264
• Main Authors: He, Qi-Ming, Zhang, Hanqin
• Format: Journal Article
• Language: English
• Published: Milano Springer Nature B.V 01.12.2007
• Subjects: Mathematics; Matrix; Theorems
• ISSN: 0008-0624; 1126-5434
• DOI: 10.1007/s10092-007-0139-7

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]