Definition:Laplace Distribution
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Definition
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X = \R$.
Let $\mu$ be a real number.
Let $b$ be a strictly positive real number.
$X$ is said to have a Laplace distribution with parameters $\mu$ and $b$ if and only if it has probability density function:
- $\map {f_X} x = \dfrac 1 {2 b} \map \exp {- \dfrac {\size {x - \mu} } b}$
This is written:
- $X \sim \map {\operatorname {Laplace} } {\mu, b}$
Also see
- Results about the Laplace distribution can be found here.
Source of Name
This entry was named for Pierre-Simon de Laplace.
Sources
- Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LaplaceDistribution.html