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The Algebraic Degree of Phase-Type Distributions

  • Mark Fackrell (a1), Qi-Ming He (a2), Peter Taylor (a1) and Hanqin Zhang (a3)

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.

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Copyright

Corresponding author

Postal address: Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.
∗∗ Current address: Department of Management Sciences, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada. Email address: q7he@uwaterloo.ca
∗∗∗ Postal address: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080 Beijing, P. R. China.

References

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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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