Normal Distribution

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Normal Distribution

The well known bell shaped curve. According to the Central Limit Theorem, the probability density function of a large number of independent, identically distributed random numbers will approach the normal distribution. In the fractal family of distributions, the normal distribution only exists when alpha equals 2, or the Hurst exponent equals 0.50. Thus, the normal distribution is a special case which in time series analysis is quite rare. See: Alpha, Central Limit Theorem, Fractal Distribution.
Copyright © 2012, Campbell R. Harvey. All Rights Reserved.

Bell Curve

A curve on a chart in which most data points cluster around the median and become less frequent the farther they fall to either side of the median. When plotted on a chart, a bell curve looks roughly like a bell.
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References in periodicals archive ?
The original Landau hydrodynamic model is, to our best knowledge, the only model suggesting some certain shape for pseudorapidity distributions of produced particles in both nucleon-nucleon and nucleon-nucleus collisions at very high energies, Gaussian distribution. Of course, it is necessary to note that only in the case of a very high multiplicity does the pseudorapidity distribution of produced particles in an individual event become a meaningful concept.
Impact of the number of the Gaussian distributions on localization accuracy Number of the Gaussian distributions Localization error (%) 2 0.383 3 0.352 4 0.349 5 0.345 6 0.342 7 0.34 8 0.338 Note: Table made from bar graph.
The Euclidean distance (dissimilarity) is most frequently used by the k-means family, and, moreover, is derived using the log likelihood of an isotropic Gaussian distribution. Therefore, the k-means using the Euclidean distance will be able to appropriately partition data sampled from isotropic Gaussian distributions but not other distributions.
The method has several advantages: (1) the outcome of the region growing approach is provided automatically as the initial contour of level set evolution method; (2) the global Gaussian distribution with different means and variances is integrated into level set framework.
In some schemes the noise is added without concerning the covariance of the data, but the uniform distribution or Gaussian distribution is directly declared [12, 13].
Some causal processes can simulate Gaussian distribution.
The GMM algorithm has been proposed by Stauffer and Grimson, [15], with the target of efficiently dealing with multimodal Bg by using a statistical model composed by a mixture of Gaussian distributions. The GMM algorithm has been modified and included in the OpenCV libraries.
He later called the Gaussian distribution "a model child," one "which is commonly called 'normal,' but in fact deserves less and less to be considered as such."
We add a little zero mean Gaussian noise to this to get the action which we actually perform [a.sub.t] = [a.sup.opt.sub.t] + [mu] where [mu] is drawn from a zero mean Gaussian distribution. It has been found essential for accurate convergence that [mu] is very small in magnitude so typically [mu] ~ N(0, 0.01).
The software quickly calculates: (a) the mean value and the standard deviation of all the measurement values; (b) the Log-Normal distribution; (c) the Gaussian distribution; (d) the deviations from the Log-Normal and Gaussian distributions in terms of the Kolmogoroff-Smirnov and Chi-square tests; (e) skewness; and (f) excess of the measured distribution.
In addition, we assume that both the spatial and the unstructured variability have Gaussian distributions, which are independent in the latter case.