The Poisson distribution was introduced by Simone Denis Poisson in 1837. It has since been subject of numerous publications and practical applications. The purpose of this paper is to raise awareness of numerous application opportunities and to provide more complete case coverage of the Poisson distribution. First a formal definition and basic characteristics of a Poisson variable and its distr...

The Poisson binomial distribution is the distribution of the sum of independent and non-identical random indicators. Each indicator follows a Bernoulli distribution with individual success probability. When all success probabilities are equal, the Poisson binomial distribution is a binomial distribution. The Poisson binomial distribution has many applications in different areas such as reliabil...