Three Fundamental Distributions: Binomial, Gaussian, and Poisson

Abstract

There are three distributions that play a fundamental role in statistics. The binomial distribution describes the number of positive outcomes in binary experiments, and it is the “mother” distribution from which the other two distributions can be obtained. The Gaussian distribution can be considered as a special case of the binomial, when the number of tries is sufficiently large. For this reason, the Gaussian distribution applies to a large number of variables, and it is referred to as the normal distribution. The Poisson distribution applies to counting experiments, and it can be obtained as the limit of the binomial distribution when the probability of success is small.