# Definition:Laplace Distribution

## 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.