PHASE-TYPE DISTRIBUTIONS AND INVARIANT POLYTOPES

被引：37
|
作者：
OCINNEIDE, CA [1 ]
机构：
[1] LOUISIANA STATE UNIV,BATON ROUGE,LA 70803
来源：
ADVANCES IN APPLIED PROBABILITY | 1991年 / 23卷 / 03期
关键词：
REPRESENTATIONS OF PHASE-TYPE DISTRIBUTIONS; TRIANGULAR REPRESENTATIONS; MARKOV CHAINS; LAPLACE TRANSFORMS; GENERATORS; BOUNDS ON EIGENVALUES;
D O I：
10.2307/1427620
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
引用
收藏
页码：515 / 535
页数：21
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