The Law of the Iterated Logarithm in Probability Theory

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The relative frequency of successes is simulated for 1,000,000 trials, and is plotted against a log scale for the number of trials. As the number of trials increases the relative frequency is observed to remain within the funnel-shaped region described by the law of the iterated logarithm, and only in rare cases will it land outside the funnel.

Contributed by: Tomas Garza (March 2011)
Open content licensed under CC BY-NC-SA


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The main reference for this topic is W. Feller, "Unlimited Sequences of Bernoulli Trials: The Law of the Iterated Logarithm," An Introduction to Probability Theory and Its Applications, Vol. 1, New York: John Wiley & Sons, Inc., 1970 pp. 204–208.



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