Stats & Stuff

The Law of Large Numbers

The Law of Large Numbers for the Binomial Distribution

An interesting aspect of statistics is the behaviour of distributions as their parameters approach infinity. Under certain conditions, some distributions will converge towards another known distributions. The central limit theorem is an example of this, which states that for a given distribution: As the number of events in a sample increases, the mean of the sample will approach the true mean of the distribution. This site has some simulations that demonstrate this convergent behaviour for the binomial theorem.

To apply the normal approximation to a binomial distribution, the following conditions must be fulfilled:

Normal Approximation to a Binomial distribution

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The law of rare events describes the conditions under which a binomial distribution converges to a poisson distribution. As the number of trials in a binomial distribution increases, the distribution converges to the poisson distribution with a corresponding mean equal to np. To use this approximation in an applied context, the following conditions must be met to apply the approximation:

This approximation is computationally simple compared to the binomial distribution it approximates for a large number of trials. Fill out the information below to see the pdf of a binomial distribution and its corresponding poisson approximation.

Law of Rare Events

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