# Laplace Distribution ```toc ``` - PDF ![[Pasted image 20240828105230.webp]] - $f(x\mid \mu ,b)={\frac {1}{2b}}\exp \left(-{\frac {|x-\mu |}{b}}\right)$ - where $\mu$ is a location parameter, and $b>0$ which is sometimes referred to as the "diversity", is a scale param If μ=0 and b=1 the positive half-line is exactly an [[Exponential Distribution.md]] scaled by 1/2 - Kinda like [[Normal Distribution.md]] but normal distribution is expressed in terms of the squared difference from the mean μ, the Laplace density is expressed in terms of the absolute difference from the mean