central limit theorem

(redirected from Lyapunov condition)
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cen·tral lim·it the·o·rem

the sum (or average) of n realizations of the same process, provided only that it has a finite variance, will approach the gaussian distribution as n becomes indefinitely large. This theory provides a broad warrant for the use of normal theory even for nongaussian data. In the form stated here, it constitutes the classical version; more general versions allow serious relaxation of the usual assumptions.
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References in periodicals archive ?
The w groups of sequence of random variables [Y.sub.ki] (1 [less than or equal to] K [less than or equal to] [omega]) satisfy the Lyapunov condition; that is [there exists][[xi].sub.k] > 0 satisfy the following formula:
That is, for layer [omega], [[xi].sub.w]([[xi].sub.[omega]] = 1) satisfies the formula (14) in Theorem 8 to make [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [Y.sub.[omega]i] also satisfies the Lyapunov condition. According to [28], [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] meets the application conditions of central limit theorem; that is, [??]([S.sub.[omega]t]) obeys the normal distribution.
To make this energy function stable and control the DC-bus voltage, it should satisfy Lyapunov conditions. The first and the second conditions are satisfied.