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.
References in periodicals archive ?
A presupposition for the standard RCV calculation is that the expected percentage change between samples follows a normal distribution (or that an appropriate transformation to achieve this can be found).
hypothesis that GDP and Population follow a log normal distribution. We do reject the hypothesis that Per Capita GDP follows a log normal distribution.
The first one is calculated assuming normal distribution of expected inflation and official current inflation as a measure of perceived inflation.
In Pacey's platoon dispersion model, the speed is assumed following normal distribution ranging from negative to positive infinity, which does not properly reflect the field situation.
In previous work [12] it was proved that in the case when the diameter of nanofibres is distributed in compound distribution from several normal distributions, the modal value of the first distribution and the percentage quantity of measurements of the first distribution can be used as a criterion of nanofibres diameter and measurement dispersion estimation.
To make the overly erratic data fit into a normal distribution model, says Bar-Yam, economists and finance quants often add complicated parameters and conditions to their models, replete with confusing terminology like heteroscedasticity and kurtosis, but all that does is cover a much simpler flaw.
The objective of this article is to illustrate how left-censored bivariate data (i.e., longitudinal data with observations < LOD for an analyte measured on two different occasions, or cross-sectional data with observations < LOD for two different analytes) can be imputed based on a bivariate normal distribution and analyzed using an MI approach.
When determining the quantile of free distribution, there is a possibility of using other than normal distributions, which can eliminate the imperfections of normal distribution during the estimation of financial time series.
Each of the distributions listed in the first column, from which sample 1 was drawn, was paired with a normal distribution, from which sample 2 was drawn.
Figures 1-3 show examples of the frequent spectra which came from the normal distributions being affected by two, three, and four perturbing factors (the progression coefficients [q.sub.i]).
Bhattacharya's method for estimating parameters for a mixture of normal distributions is well described by Sparre & Venema (1992).
The values for kurtosis relate to leptokurtic distributions, which exhibit fat tails and high peaks with respect to normal distributions. When considering a possible nonnormal distribution characterized by negative asymmetry and fat tails, a situation of higher probabilities for extreme negative returns emerges than would in the case of a normal distribution.