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Fitting with Matrix-Exponential Distributions.
- Source :
- Stochastic Models; May2005, Vol. 21 Issue 2/3, p377-400, 24p, 4 Graphs
- Publication Year :
- 2005
-
Abstract
- It is well known that general phase-type distributions are considerably overparameterized, that is, their representations often require many more parameters than is necessary to define the distributions. In addition, phase-type distributions, even those defined by a small number of parameters, may have representations of high order. These two problems have serious implications when using phase-type distributions to fit data. To address this issue we consider fitting data with the wider class of matrix-exponential distributions. Representations for matrix-exponential distributions do not need to have a simple probabilistic interpretation, and it is this relaxation which ensures that the problems of overparameterization and high order do not present themselves. However, when using matrix-exponential distributions to fit data, a problem arises because it is unknown, in general, when their representations actually correspond to a distribution. In this paper we develop a characterization for matrix-exponential distributions and use it in a method to fit data using maximum likelihood estimation. The fitting algorithm uses convex semi-infinite programming combined with a nonlinear search. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15326349
- Volume :
- 21
- Issue :
- 2/3
- Database :
- Complementary Index
- Journal :
- Stochastic Models
- Publication Type :
- Academic Journal
- Accession number :
- 17539955
- Full Text :
- https://doi.org/10.1081/STM-200056227