Definition: Poisson distribution

Index: The Book of Statistical Proofs ▷ Probability Distributions ▷ Univariate discrete distributions ▷ Poisson distribution ▷ Definition

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 $\lambda > 0$.

 

Sources:

• 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.