Laplace Distribution

The Laplace (or Double Exponential) distribution has density function:

f(x) = 1/(2b)*e-|x-a|/b        -∞<x<∞

where

a

is the mean of the distribution

b 

is the scale parameter

e

is the base of the natural logarithm, sometimes called Euler's e (2.71...)

 

The graphic above shows the shape of the Laplace distribution when the location parameter equals 0 and the scale parameter equals 1, 2, 3, and 4. For a complete listing of all distribution functions, see Distributions and Their Functions.