In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also known as the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together back-to-back. The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution, as is a Brownian motion evaluated at an exponentially distributed random time.

The probability density function of the gamma distribution is

f(x,mu,sigma) = 1/(2s)exp(-abs(x-mu)/s)

where   

s = sigma/sqrt(2)

support -Inf ⇐ x ⇐ Inf