Normal Distribution

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Related to Gaussian random variable: Normal random variable, Gaussian density

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 ?
In the derivation of the proposed detection schemes, it is claimed that the effect of CSI errors, [Ex.sub.k], can be approximately modeled as Gaussian random variables under the assumption that [N.sub.t] is sufficiently large, and its proof is given in Appendix A.
where [v'.sub.kn] is a Gaussian random variable with zero mean and [[summation].sup.N-1.sub.n=0] [[absolute value of [[beta].sub.n](k[T.sub.s])].sup.2] [[sigma].sup.2.sub.w] variance.
Therefore, an application of theoretical bit error rate curves based on the consideration that interference is Gaussian random variable, and cannot be recommended for such spreading sequences.
Gaussian random variables with mean zero and variance [[sigma].sup.2.sub.[empty set]], the entries of the noise vector are i.i.d.
It could be shown that in all of the random variables with unit variance, Gaussian random variable has the most entropy.
Invoking the central limit theorem, the interference plus noise could be considered as a complex Gaussian random variable z with variance [[sigma].sup.2.sub.z] = [6.summation over (j=1)][6.summation over (i=0)][L.sup.(j).sub.i][P.sup.(j).sub.i] + [[sigma].sup.2.sub.n].
The demand of remaining buses (not presented in Table II) are assumed to be Gaussian random variables, with standard deviation fixed at 5% of the mean value.
Polynomial chaos was first introduced by Wiener [6] where Hermite polynomials were used to model stochastic processes with Gaussian random variables. A number of other expansions have been proposed in the literature for representing non-Gaussian process [7, 8].
Therefore, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is Gaussian because the sum of independent Gaussian random variables is also Gaussian.
where [mu] is a drift term and [[epsilon].sub.t] is a sequence of independent and identically zero-mean Gaussian random variables. Let the year of birth be equal to c = t - x.

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