Asymptotic distribution

Asymptotic distribution

In mathematics and statistics, an asymptotic distribution is a hypothetical distribution that is in a sense the "limiting" distribution of a sequence of distributions. A sequence of distributions corresponds to a sequence of random variables

:Zi

for "i" = 1, 2, ..... An asymptotic distribution exists if the probability distribution of Zi converges to a probability distribution (the asymptotic distribition) as "i" increases. If an asymptotic distribution exists, it is not necessarily true that any one outcome of the sequence of random variables is a convergent sequence of numbers. It is the sequence of probability distributions that converges.

A special case of an asymptotic distribution is when the sequence of random variables always approachs zero -- that is, the Zi go to 0 as i goes to infinity. Here the asymptotic distribution is a degenerate distribution, corresponding to the value zero.

The central limit theorem provides an example where the asymptotic distribution is the normal distribution.

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