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normal distribution
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normal distribution

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A curve used in statistics to represent the distribution of data which is symmetrical about its mean value.

In statistics, a distribution widely used to model variation in a set of data which is symmetrical about its mean value. It can be expressed in the form:

where f(x) is the relative frequency of data value x, ςis the standard deviation, μ is the mean, exp is the exponential function, and π is a mathematical constant. The curve resulting when f(x) is plotted against x is called the normal distribution curve.

An example of normal distribution can be found in the intelligence quotients (IQs) found in human populations, distributed around a mean value of 100. The distribution is also known as the Gaussian distribution after German mathematician Karl Gauss.
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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.
Error and bias in determining exposure potential of children at ... by Zandbergen, Paul A.; Green, Joseph W. / Environmental Health Perspectives
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.
Powder diffraction: least-squares and beyond by David, W.I.F. / Journal of Research of the National Institute of Standards and Technology
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).
Fat--tails and VaR estimation using power EWMA models by Lee, Hsien-Feng / Journal of Academy of Business and Economics
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