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Discrete-Time Stochastic Systems
Published in Raymond G. Jacquot, Modern Digital Control Systems, 2019
The variance is the second central moment, or () σw2(k)=E{[w(k)−w¯(k)]2}=∫−∞∞[w−w¯(k)]2pw(w,k)dw
Spectral Density
Published in David C. Swanson, ®, 2011
The variance is defined as the second central moment, or the mean-square value minus the mean value-squared. The standard deviation for the random variable, σY, is the square root of the variance. () σY2=Y¯2−mY2=∫−∞+∞(y−mY)2pY(y)dy
Probability Theory
Published in A. C. Faul, A Concise Introduction to Machine Learning, 2019
The forth normalized central moment is the kurtosiskurtosis and measures how heavy tailed the probability distribution is. It is derived from the Greek word for “arching”. A large value of the kurtosis means that extreme values of the random variable are more likely, while a small value of kurtosis means outliers are rare.
Optimization-Based Hybrid Intelligent Model for Decision Making on Electrical Discharge Machining (EDM) Process of A6061/6%B4C and A6061/9%SiC Composite Materials
Published in Cybernetics and Systems, 2023
C. S. Shyn, R. Rajesh, M. Dev Anand
The central moment in probability theory and statistics refers to the moment of the probability distribution with the random variable. (In percent probability, theory, and statistics, random percent variable, from percent the mean; Pébay et al. 2016). The characteristics of a probability distribution were used to determine various seconds from the numbers of one set. The core moments are used to calculate deviations from the mean that are greater than zero, with reference to the normal moments. The greater moments only have an impact on the prevalence of the location and shape distribution. moment of actual number arbitrary word was total where, ➔ “expectation operator”. moment of mean was displayed probability density function (PDF). A moment is displayed in Equation (1)
Multi-modal classifier fusion with feature cooperation for glaucoma diagnosis
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2019
Nacer Eddine Benzebouchi, Nabiha Azizi, Amira S. Ashour, Nilanjan Dey, R. Simon Sherratt
Moments are scalar quantities used to describe a function and to capture its important characteristics. The moments notion in mathematics, are projections of a function on a polynomial basis; different systems of moments can be recognized according to the polynomial base used. The Central Moments have become one of the most used shape descriptors in many fields (Angshuman, Nilotpal, & Ananda, 2012; Luxin, Mingzhi, Houzhang, Hai, & Tianxu, 2012; Saeed, Karim, & Farshid, 2006), which have shown superior performance. A central moment is a moment of a probability distribution of a random variable on the mean of the random variable. Geometric moment (raw moment) of order (p + q) for a 2-dimensional discrete function is calculated as follows:
A comparison of building energy optimization problems and mathematical test functions using static fitness landscape analysis
Published in Journal of Building Performance Simulation, 2019
Christoph Waibel, Georgios Mavromatidis, Ralph Evins, Jan Carmeliet
With the LP sequence, we have obtained large samples of the problems, which we can use to plot the fitness distribution in the form of histograms in Figures 10 and 11 (Malan and Engelbrecht 2013; Reid 2015). This informs us of the probability densities of the cost values, i.e. the frequency at which each cost value occurs, from which we can infer the difficulty for finding low cost solutions. We compute the second central moment, i.e. the variance, of this distribution: where is the expected value, are the cost values of the sequence X after mean normalization, and is the mean of y. A large variance indicates a higher distribution of cost values, whereas a small variance indicates that there is a smaller range of frequent cost values.