Author

• D. R. McDonald

Abstract

The local limit theorem describes how the density of a
sum of random variables follows the normal curve. However the local
limit theorem is often seen as a curiosity of no particular importance
when compared with the central limit theorem. Nevertheless the local
limit theorem came first and is in fact associated with the foundation
of probability theory by Blaise Pascal and Pierre de Fermat and was
originally formalized by Jakob Bernoulli, Abraham DeMoivre and
Pierre-Simon Laplace.
Here we describe the historical roots of the local limit theorem.
We describe how it was supplanted by the central limit theorem in
applications. Then we review the revival started by B. V. Gnedenko
and we describe modern developments.

Keywords

• historical study
• local limit theorem