The Law of the Iterated Logarithm
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The central limit theorem tells us that suitably normalized sums can be approximated by a normal distribution. Although arbitrarily large values may occur, and will occur, one might try to bound the magnitude in some manner. This is what the law of the iterated logarithm (LIL) does, in that it provides a parabolic bound on how large the oscillations of the partial sums may be as a function of the number of summands.
KeywordsCentral Limit Theorem Independent Random Variable Iterate Logarithm Normal Random Variable Exponential Bound
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