Sample Sizes and the Central Limit Theorem: The Poisson Distribution as an Illustration

Abstract

Poisson distributions are often used to show that the central limit theorem is valid even for discrete and for highly skewed distributions. It is not so commonly appreciated that they can also be used to demonstrate that, in some cases, very large sample sizes may not be enough to invoke the theorem. Binomial distributions can be used in a similar manner.

Key Words:

• Binomial distribution
• Central limit theorem
• Poisson distributions
• Sample sizes