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The 27 pages that link to Poisson distribution, each with the reason it gives.

• Random variableBroader topic: It models event counts in settings where events occur independently at a stable average rate.

• Probability distributionBroader topic: It models event counts and approximates binomial probabilities under suitable rare-event conditions.

• Exponential functionRelated: Its probability formula uses an exponential factor to normalize event-count probabilities.

• FactorialRelated: Its probability formula includes k! in the denominator.

• Binomial distributionCompared with: It approximates binomial counts when trials are numerous and success probability is small.

• Probability mass functionBroader topic: Its mass function models counts of events in settings with a fixed average rate.

• Exponential distributionRelated: Poisson counts and exponential waiting times are two descriptions of the same event process.

• Geometric distributionCompared with: It counts events over a fixed interval rather than trials until a first success.

• 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.

• Negative binomial distributionCompared with: It provides a different count model and a limiting approximation when successes are rare.

• Falling factorialRelated: Its factorial moments use falling factorials and have especially simple values.

• Siméon Denis PoissonBroader topic: This distribution bears Poisson’s name and formalizes rare-event counts.

• Chi-squared distributionCompared with: It models counts directly, whereas chi-squared procedures often approximate statistics built from counts.

• Poisson regressionRelated: It supplies the standard response distribution and variance assumption for the model.

• Poisson limit theoremBroader topic: This is the limiting distribution as binomial trials become numerous and individually unlikely.

• Lehmann–Scheffé theoremRelated: For independent Poisson observations, their sum is complete and sufficient for the common rate.

• Lotka's lawCompared with: Its comparatively thin tail differs from the high-productivity tail described by Lotka's law.

• Poisson point processRelated: Counts in each finite-measure region follow this distribution, with parameter equal to its intensity.

• Erdős–Kac theoremCompared with: Individual prime divisibility is rare, but the growing collection of primes produces a normal rather than fixed Poisson limit.

• 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.

• Hellin's lawCompared with: It offers a formal count model, unlike Hellin's simple empirical powers-of-89 pattern.

• Law of Truly Large NumbersRelated: For many trials with small probabilities, it approximates the count of rare occurrences.