ICA by PCA Approach: Relating Higher-Order Statistics to Second-Order Moments

2006 ◽  
pp. 311-318 ◽  
Author(s):  
Kun Zhang ◽  
Lai-Wan Chan
Keyword(s):  
Order Statistics ◽  
Higher Order ◽  
Second Order ◽  
Higher Order Statistics

Propagating Skewness and Kurtosis Through Engineering Models for Low-Cost, Meaningful, Nondeterministic Design

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Travis V. Anderson ◽  
Christopher A. Mattson
Keyword(s):  
Order Statistics ◽  
Taylor Series ◽  
Computational Cost ◽  
Higher Order ◽  
Second Order ◽  
System Model ◽  
Higher Order Statistics ◽  
Actual System ◽  
System Output ◽  
Skewness And Kurtosis

System models help designers predict actual system output. Generally, variation in system inputs creates variation in system outputs. Designers often propagate variance through a system model by taking a derivative-based weighted sum of each input’s variance. This method is based on a Taylor-series expansion. Having an output mean and variance, designers typically assume the outputs are Gaussian. This paper demonstrates that outputs are rarely Gaussian for nonlinear functions, even with Gaussian inputs. This paper also presents a solution for system designers to more meaningfully describe the system output distribution. This solution consists of using equations derived from a second-order Taylor series that propagate skewness and kurtosis through a system model. If a second-order Taylor series is used to propagate variance, these higher-order statistics can also be propagated with minimal additional computational cost. These higher-order statistics allow the system designer to more accurately describe the distribution of possible outputs. The benefits of including higher-order statistics in error propagation are clearly illustrated in the example of a flat-rolling metalworking process used to manufacture metal plates.

Evaluation of a new Power Quality index, based in Higher Order Statistics

2017 ◽  
Vol 1 (15) ◽  
pp. 37-42
Author(s):  
J.M. Sierra-Fernández ◽  
J.J. González De La Rosa ◽  
A. Agüera-Pérez ◽  
J.C. Palomares Salas ◽  
O. Florencias-Oliveros
Keyword(s):  
Order Statistics ◽  
Power Quality ◽  
Quality Index ◽  
Higher Order ◽  
Higher Order Statistics
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