Asymptotic Distribution - Asymptotic Normality

Asymptotic Normality

Perhaps the most common distribution to arise as an asymptotic distribution is the normal distribution. In particular, the central limit theorem provides an example where the asymptotic distribution is the normal distribution.

Barndorff-Nielson & Cox provide a direct definition of asymptotic normality.

The Binomial distribution seems to be the first asymptotic approximation by a normal distribution; compared to the more general case of central limit theorem, convergence of the Binomial to the normal is especially rapid. Asymptotic normality of the Binomial distribution is proven by the de Moivre–Laplace theorem.