Central limit theorem

Central limit theorems are a set of weak-convergence results in probability theory. Intuitively, they all express the fact that any sum of many independent identically distributed random variables will tend to be distributed according to a particular "attractor distribution". The most important and famous result is simply called The Central Limit Theorem which states that if the summed variables have a finite variance then they will be approximately normally distributed. Since many real processes yield distributions with finite variance, this explains the ubiquity of the normal distribution.

Non-independent case

There are some theorems which treat the case of sums of non-independent variables, for instance the m-dependent central limit theorem, the martingale central limit theorem and the central limit theorem for mixing processes.

Related Topics:
M-dependent central limit theorem - Martingale central limit theorem - Central limit theorem for mixing processes

~ ~ ~ ~ ~ ~ ~ ~ ~ ~