Definition: Poisson distribution
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The Book of Statistical Proofs ▷
Probability Distributions ▷
Univariate discrete distributions ▷
Poisson distribution ▷
Definition
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Metadata: ID: D62 | shortcut: poiss | author: JoramSoch | date: 2020-05-25, 23:34.
Definition: Let $X$ be a random variable. Then, $X$ is said to follow a Poisson distribution with rate $\lambda$
\[\label{eq:poiss} X \sim \mathrm{Poiss}(\lambda) \; ,\]if and only if its probability mass function is given by
\[\label{eq:poiss-pmf} \mathrm{Poiss}(x; \lambda) = \frac{\lambda^x \, e^{-\lambda}}{x!}\]where $x \in \mathbb{N}_0$ and $\lambda > 0$.
- Wikipedia (2020): "Poisson distribution"; in: Wikipedia, the free encyclopedia, retrieved on 2020-05-25; URL: https://en.wikipedia.org/wiki/Poisson_distribution#Definitions.
Metadata: ID: D62 | shortcut: poiss | author: JoramSoch | date: 2020-05-25, 23:34.