Phase distributions: Selecting parameters to match moments
Abstract
The family of phase distributions is an important tool in algorithmic probability. Despite the wide-spread use of phase distributions in computationally tractible stochastic models, the phase-distribution-selection problem has been largely ignored. The lack of methods for selecting phase distributions that accurately reflect the randomness of modelled processes limits the practical utility of phase distributions. The objective of the author's dissertation research is to provide methods for selecting appropriate phase distributions. In particular, methods for matching three moments to phase distributions are developed and evaluated. The methods developed by the author take advantage of properties of special classes of phase distributions to match moments analytically or via nonlinear programming techniques. Evaluation of the methods is based on properties of moment-matching algorithms and of phase distributions selected by the algorithms. Primary attributes of algorithms are efficiency, suitability for automation, and flexibility. Important properties of selected distributions include dimension, density-function shape, numerical stability, and special structure. Also, the appropriateness of the three-moment partial characterization and of some three-moment-matching algorithms for use in queueing approximators is examined. A moment-matching algorithm for queueing approximations is then proposed.
Degree
Ph.D.
Advisors
Taaffe, Purdue University.
Subject Area
Industrial engineering
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