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 ?
alpha]/2] denotes the upper [alpha]/2 quantile of the standard normal distribution, i.
It should be noted that since FOSA does not transform the limit state from the original space to the standard normal space, it is expected to be more accurate than FORM in which the accuracy may be reduced when the transformation increases the nonlinearity of the limit state function.
The value of the standard normal distribution is calculated from the applied load, the adjusted basic strength, and the standard deviation of the total performance strength.
The Y axis of cumulative standard normal distribution is divided into two parts by Moro algorithm, and then takes two corresponding algorithms for processing.
where t = ln L - [mu] / [sigma] and [PHI](t) is the cdf of the standard normal distribution.
for conditions i in the second group, where z(r) are standard normal random numbers.
with g [not equal to] 0, h [member of] R, where the distribution of Z is standard normal.
is the w-variate standard normal cdf, and [theta] is an (m x m) matrix with dependence terms in the off-diagonal.
In case of an analysis of an adequate number of samples, the deviations will be typically situated along the probability density function of a standard normal unimodal distribution (figure 3).
For each day type, a vector of twelve standard normal random numbers was created, r.
Where [PHI] is the cdf of the standard normal distribution?
This will generate a standard normal deviate centered on 0 with a range of -6 to 6.

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