Definition: Exponential distribution

Index: The Book of Statistical Proofs ▷ Probability Distributions ▷ Univariate continuous distributions ▷ Exponential distribution ▷ Definition

Definition: Let $X$ be a random variable. Then, $X$ is said to be exponentially distributed with rate (or, inverse scale) $\lambda$

\[\label{eq:exp} X \sim \mathrm{Exp}(\lambda) \; ,\]

if and only if its probability density function is given by

\[\label{eq:exp-pdf} \mathrm{Exp}(x; \lambda) = \lambda \exp[-\lambda x], \quad x \geq 0\]

where $\lambda > 0$, and the density is zero, if $x < 0$.

 

Sources:

• Wikipedia (2020): "Exponential distribution"; in: Wikipedia, the free encyclopedia, retrieved on 2020-02-08; URL: https://en.wikipedia.org/wiki/Exponential_distribution#Definitions.

Metadata: ID: D8 | shortcut: exp | author: JoramSoch | date: 2020-02-08, 23:48.