Three Fundamental Distributions: Binomial, Gaussian, and Poisson

Abstract

There are three distributions that play a fundamental role in statistics. The binomial distribution is used to describe binary experiments, and it is in many respects the mother distribution from which the other two distributions can be obtained. The Gaussian or normal distribution can be considered as a special case of the binomial when the number of tries of the experiment is sufficiently large. Its central role in probability and statistics is due to the central limit theorem, which is presented in Chap. 4. The Poisson distribution applies to integer-valued counting experiments, and it can be obtained as a limit of the binomial distribution when the probability of success is small. Although there are several more distributions that are of common use, these three distributions are central to many of the methods presented in this textbook, and they are therefore presented in more detail.