Central Limit Theorem


Also found in: Dictionary, Medical, Acronyms, Wikipedia.

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.
Mentioned in ?
References in periodicals archive ?
SAMPLING DISTRIBUTION OF THE MEAN AND THE CENTRAL LIMIT THEOREM
Below is the Matlab code used to perform the application of the Central Limit Theorem.
Finite-range dependence implies the mixing conditions that ensure the central limit theorem in Equation (3).
Applications of the central limit theorem exist in the gaming literature as well.
Laplace discovered that the means are distributed approximately according to the normal curve and the Central Limit Theorem is sometimes known as the "normal law of random errors.
There has been much confusion in the insurance economics literature with regard to the implications of the law of large numbers and the central limit theorem.
Lee (1996), The central limit theorem for weighted minimal spanning trees on random points, Ann.
Note that without a numerical value for C, the result, while providing information about the rate of convergence in the central limit theorem, does not provide an answer to the undergraduate question mentioned above.
In order to prove the central limit theorem we go back to (2) and similarly expand the integral
Hwang, On convergence rates in the central limit theorems for combinatorial structures, European J.
Working from the assumption readers have completed a first- or second-year undergraduate course in analysis, which included some work in measure theory, Lesigne covers modeling an experiment in probability, random variables, independence, binomial distribution, the strong and weak laws of large numbers, the large deviation estimate, the central limit theorem, the moderate deviations estimate, the local limit theorem, the arcsine law, the law of iterated logarithm, and the recurrence of random walks.

Full browser ?