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Normal Distribution
(redirected from Error Distribution)

   Also found in: Medical, Encyclopedia, Wikipedia, Hutchinson 0.04 sec.
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.


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Statistics Centerlines TIGER Firm A Firm B Mean 219 351 300 461 Median 155 178 153 151 Standard deviation 272 604 602 2,330 Minimum 50 49 48 39 Maximum 2,302 4,379 5,565 2,596 90th percentile 211 271 238 218 95th percentile 227 302 255 237 95% RMSEa 196 306 235 210 (a) 95% RMSE is the root mean square error of the error distribution after removing 5% outliers.
The underlying principles of probability theory indicate that least-squares analysis is appropriate only if (i) the data points have an associated Gaussian error distribution and (ii) the proposed model is a complete representation of the observed data.
The Power EWMA estimator is based on the maximum likelihood estimator of the variance of the power exponential distribution (also known as the generalized error distribution, or Box-Tiao distribution).
 
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