Poisson Distribution

CORE DEFINITION

The Poisson distribution (French: loi de Poisson; English: Poisson distribution), also known as Poisson distribution, Poisson distribution, Bois de Boulogne distribution, Bouasson distribution, Puasson distribution, Poisson distribution, Bu's distribution, and Poisson law of small numbers, is a discrete probability distribution commonly seen in statistics and probability theory. It was published by the French mathematician Siméon Denis Poisson in 1838. The Poisson distribution is suitable for describing the probability distribution of the number of random events occurring in a unit time. For example, the number of service requests received by a service facility in a certain period, the number of calls received by a telephone exchange, the number of passengers waiting at a bus stop, the number of machine failures, the number of natural disasters, the number of mutations in DNA sequences, the number of decays of radioactive atomic nuclei, the distribution of photon numbers in lasers, etc. (The number of occurrences per unit time can be regarded as the frequency of event occurrence, similar to physical frequency. f. {\displaystyle f}.). The probability mass function of the Poisson distribution is: P.