What is the Poisson distribution continuously analog

Glossary entry

The Poisson distribution is a one-parameter and discrete probability distribution. It is also known as the "distribution of rare events". The Poisson distribution results when the limit value for n towards infinity and p towards 0 is formed from a binomial distribution while keeping the product of n and p constant.

To describe the Poisson distribution, only one parameter is required, the μ (also referred to in the literature as λ).

The Poisson distribution is named after the mathematician Siméon Denis Poisson, who, however, did not discover or define it. The Poisson distribution is a discrete probability distribution that can be used to model or describe the number of events that occur at a constant rate and independently of one another in a fixed time interval or spatial area. Example: the number of volcanic eruptions in a defined time interval or the number of bad debts within a year.

Analogous to the binomial distribution, the Poisson distribution predicts the expected result of a series of Bernoulli experiments (random experiments).

For example, the Poisson distribution allows the calculation of the probability that no lightning will strike, but the question of how often the lightning does not strike does not make sense because of the continuous observation.