KnowraPoisson distributionLinked fromLinked fromThe 27 pages that link to Poisson distribution, each with the reason it gives.All 27Broader topic 5Related 15Compared with 7Exponential functionRelated: Its probability formula uses an exponential factor to normalize event-count probabilities.FactorialRelated: Its probability formula includes k! in the denominator.Exponential distributionRelated: Poisson counts and exponential waiting times are two descriptions of the same event process.Poisson processRelated: The number of events in an interval of length t has this distribution with mean rate times t.Method of momentsRelated: Its mean equals its rate parameter, so the sample mean supplies an estimate.Stirling numbers of the second kindRelated: Its raw moments are Touchard polynomials, and therefore involve Stirling numbers.Coherent stateRelated: Measurements of particle number in a coherent state follow this distribution.Exponential generating functionRelated: Its probability weights visibly contain factorials, though the distribution is not itself an exponential generating function.Falling factorialRelated: Its factorial moments use falling factorials and have especially simple values.Poisson regressionRelated: It supplies the standard response distribution and variance assumption for the model.Lehmann–Scheffé theoremRelated: For independent Poisson observations, their sum is complete and sufficient for the common rate.Poisson point processRelated: Counts in each finite-measure region follow this distribution, with parameter equal to its intensity.Le Cam's theoremRelated: It supplies the approximating distribution, with mean matching the Bernoulli sum.Exponential networkRelated: The Erdős–Rényi random graph has an approximately Poisson degree distribution in a sparse limit.Law of Truly Large NumbersRelated: For many trials with small probabilities, it approximates the count of rare occurrences.