Introduction to Central Limit Theorem + α

In short, CLT (Central Limit Theorem) theoretically supports the intuitive phenomena.

Averaging things out tends to create a bell curve pattern, even if the original data doesn’t follow one.

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This article introduces several variants of CLTs, from classical^[1]Abraham de Moivre had the initial breakthrough for a specific case (binomial approximation), while Pierre-Simon Laplace provided the first general statement and proof that forms the core of the … Continue reading to a general formulations, along with relationships between them.

We did not get in details about stable distributions, since it involves quite a hard works to construct rigorous, but interesting discussion in row. We’ll discuss in another article, though.

Further generalizations in such a way that

• dependent variables are possible^[2]martingale difference sequences, mixing sequences, etc.;
• random functions (stochastic processes) are possible^[3]showing convergence to processes like Brownian motion..

are not our scope either.