1.Previous
3.Next

the theorem can be stated as follows:

\mathcal{N}\left(0,\sigma^2\right) .}}

In the case convergence in distribution means that the cumulative distribution functions of converge pointwise to the cdf of the distribution: for every real number

where is the standard normal cdf evaluated at The convergence is uniform in in the sense that

where denotes the supremum (i.e. least upper bound) of the set.

Lyapunov CLT

1.Previous
3.Next