NDLI: L1-Normed GM(1,1) Models and Reliability Analysis

Content Provider	IEEE Xplore Digital Library
Author	Guo, R. Cheng, C.Y. Cui, Y.H.
Copyright Year	2006
Description	Author affiliation: Univ. of Cape Town, Cape Town (Guo, R.)
Abstract	Grey theory is a mathematical branch dealing with system dynamics having sparse data availability. Grey reliability analysis is thus advantageous because of the small sample size requirements, say, the first-order one-variable grey differential equation only needs as little as four data points. However, the grey estimation of state dynamic law uses least-square approach, i.e., parameter estimation under $L_{2}$ norm. Problems associated with $L_{2}$ norm grey estimation are the model accuracy specifications. The $L_{2}$ norm grey modeling campus often borrows the model fitting criteria from statistical linear model analysis, for example, using mean-sum-of squared errors as model fitting criterion and even using probability bound for it. These exercises are putting themselves in controversy. In numerical analysis and approximation theory, relative error is a standard approximation criterion although the $L_{2}$ norm grey modeling campus also uses relative error as model accuracy measure. In this paper, we propose a $L_{1}$ norm based grey modeling and search the grey parameters in terms of simplex technique in linear programming. Grey reliability analysis under $L_{1}$ norm based grey state dynamics will be briefly discussed.
Starting Page	775
Ending Page	779
File Size	834224
Page Count	5
File Format	PDF
ISBN	1424400996
DOI	10.1109/ICSMC.2006.384481
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-10-08
Publisher Place	Taiwan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Reliability engineering Maximum likelihood estimation Cities and towns Fuzzy logic Reliability theory Approximation methods Exponential distribution Africa Modems Cybernetics
Content Type	Text
Resource Type	Article

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