# Central Limit Theorem

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## Central Limit Theorem

The Law of Large Numbers states that as a sample of independent, identically distributed random numbers approaches infinity, its probability density function approaches the normal distribution. See: Normal Distribution.

## Central Limit Theorem

In statistics, a theory stating that as the sample size of identically distributed, random numbers approaches infinity, it is more likely that the distribution of the numbers will approximate normal distribution. That is, the mean of all samples within that universe of numbers will be roughly the mean of the whole sample.
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One is the Edgeworth expansion which can incorporate weak deviation from Gaussian noises, and it has been used in various problems near the regime the central limit theorem works (17) as well as in the weakly nonlinear evolution of density fluctuations in the Universe.
Section 3 details a general version of the Functional Central Limit Theorem that covers a wide range of disturbance processes.
n] for these models have already been computed, see for instance [Bia01] and [LS77]; so the true novelty of this paper consists in the central limit theorems, see Theorems 2 and 5.
The Central Limit Theorem (CLT) states that for random samples taken from a population with a standard deviation of s (variance [s.
The central limit theorem implies that, when N is large, [S.
The program's Basic Statistics and Arithmetic section examines data distribution and leads students into the central limit theorem result, by simulation.
The topics include data and its representation, univariate random variables, important discrete probability distributions, functions of several random variables, and the central limit theorem.
Section 4 contains detail description of the functionality of the tool for visualizing the Central Limit Theorem (CLT).
The central limit theorem, in simple terms, states that the probability distribution of the mean of a random sample, for most probability distributions, can be approximated by a normal distribution when the number of observations in the sample is 'sufficiently' large.
This edition has a new chapter on one-sample tests, new exercises at the end of each chapter, more material on the central limit theorem, and places answers to practice questions in a separate appendix.
Students are introduced to true score theory, Poisson distribution, central limit theorem and directly observe the effects of sampling error.
It is a well-known fact that for bounded and identically distributed random variables (and even under much weaker conditions), one can replace the condition of independence by "m-dependence" (where m is the size of the gap needed to ensure independence of the two blocks), and this is enough to ensure that the standard central limit theorem from probability theory holds.

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