Journal ArticleDOI
A Gaussian Approximation to the Distribution of a Definite Quadratic Form
D. R. Jensen,Herbert Solomon +1 more
TLDR
In this paper, a new Gaussian approximation to the noncentral chi-square (x2) distribution is found for which the coefficient of skewness is smaller than a cube root transformation in the literature.Abstract:
Let Qk = Σk j-1 cj(xj + aj)2 be a definite quadratic form in independent standardized Gaussian variables, xj, EQk = 01. The normalizing transformation (Qk/01)h is investigated, where h is determined by the first three moments of Qk. A new Gaussian approximation to the noncentral chi-square (x2) distribution is found for which the coefficient of skewness is smaller than a cube root transformation in the literature. Our transformation specializes to the cube root transformation of Wilson and Hilferty for the central x2 distribution. The approximation is simple to apply and compares well with other approximations in a number of cases studied numerically.read more
Citations
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Journal ArticleDOI
Multivariate SPC charts for monitoring batch processes
Paul Nomikos,John F. MacGregor +1 more
TL;DR: The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered and multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches.
Proceedings ArticleDOI
Diagnosing network-wide traffic anomalies
TL;DR: A general method based on a separation of the high-dimensional space occupied by a set of network traffic measurements into disjoint subspaces corresponding to normal and anomalous network conditions to diagnose anomalies is proposed.
Journal ArticleDOI
Control Procedures for Residuals Associated With Principal Component Analysis
TL;DR: In this article, the treatment of residuals associated with principal component analysis (PCA) is discussed, i.e., the difference between the original observations and the predictions of them using less than a full set of principal components.
Proceedings Article
In-Network PCA and Anomaly Detection
TL;DR: A PCA-based anomaly detector in which adaptive local data filters send to a coordinator just enough data to enable accurate global detection is developed, based on a stochastic matrix perturbation analysis that characterizes the tradeoff between the accuracy of anomaly detection and the amount of data communicated over the network.
Journal ArticleDOI
Multivariate concentration determination using principal component regression with residual analysis.
TL;DR: A multivariate chemometric method, principal component regression, is described in a simple manner from the point of view of an analytical chemist to demonstrate the need for proper quality-control (QC) measures in multivariate analysis and to advocate the use of residuals as a proper QC method.
References
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Book
Continuous univariate distributions
TL;DR: Continuous Distributions (General) Normal Distributions Lognormal Distributions Inverse Gaussian (Wald) Distributions Cauchy Distribution Gamma Distributions Chi-Square Distributions Including Chi and Rayleigh Exponential Distributions Pareto Distributions Weibull Distributions Abbreviations Indexes
Journal ArticleDOI
Errata: Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1994, and all known reprints
K. S. Kölbig,F. Schäff +1 more
Journal ArticleDOI
Computing the distribution of quadratic forms in normal variables
TL;DR: In this paper, exact and approximate methods for computing the distribution of quadratic forms in normal variables are given for a given value x, around the probability P{Q > x}.
Journal ArticleDOI
The non-central chi2- and F-distributions and their applications.
TL;DR: In this article, the Neyman-Pearson theory of testing statistical hypotheses, the efficiency of a statistical test is to be judged by its power of detecting departures from the null hypothesis.