# Normal Distribution

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Related to Gauss distribution: Gaussian random variable

## 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.

## 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.
References in periodicals archive ?
17 demonstrates that IR-tree outperforms GR-tree and CDQO by an average of 73% and 25%, respectively, with a uniform distribution, while IR-tree outperforms GR-tree and CDQO by 80% and 27%, respectively, with a Gauss distribution. In the case of a skew distribution, IR-tree outperforms GR-tree and CDQO by 82% and 24%, respectively.
If the deviation [[epsilon].sub.k] (t) is only noise, it obeys Gauss distribution. So the preliminary criteria for outlier detection are to determine the probability that the deviation follows Gauss distribution.
It is a multi-pass filter where each pass uses results from the previous one and applies small amount of blur, accumulating enough to approximate Gauss distribution. In each pass, the new pixel value is the average of 16 samples in a rectangular pattern at variable distance from the pixel center.

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