Phase-type distributions and invariant polytopes
1991 ◽
Vol 23
(03)
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pp. 515-535
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Keyword(s):
The notion of an invariant polytope played a central role in the proof of the characterization of phase-type distributions. The purpose of this paper is to develop invariant polytope techniques further. We derive lower bounds on the number of states needed to represent a phase-type distribution based on poles of its Laplace–Stieltjes transform. We prove that every phase-type distribution whose transform has only real poles has a bidiagonal representation. We close with three short applications of the invariant polytope idea. Taken together, the results of this paper show that invariant polytopes provide a natural approach to many questions about phase-type distributions.
Keyword(s):
1985 ◽
Vol 22
(01)
◽
pp. 247-250
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1987 ◽
Vol 24
(03)
◽
pp. 696-708
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2007 ◽
Vol 14
(04)
◽
pp. 379-398
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Keyword(s):
2007 ◽
Vol 64
(6)
◽
pp. 591-611
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Keyword(s):
2013 ◽
Vol 31
(4)
◽
pp. 671-683
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Keyword(s):