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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.

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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The following several combination modes are used for simulation analysis, respectively: 1) Case 1: Both measurement error and parameters error obey normal distribution with zero mean and different variances; 2) Case 2: Measurement error obeys uniform distribution of zero mean, parameters error obeys normal distribution of zero mean; 3) Case 3: Measurement error obeys normal distribution of zero mean; parameters error obeys uniform distribution of zero mean.
Appendices include a random number table, the standard Normal distribution and critical values of several statistical distributions.
Humans would most likely live in an average bubble" only if A) the distribution of bubbles under consideration resembles a normal distribution (such that near-average examples are more likely than far from average ones) and B) the sample of studied universes is randomly selected and large enough to be statistically representative.
 
 
 
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