Laplace Distribution

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.
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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...)
Laplace Distribution (animation) 
The graphic above shows the changing shape of the Laplace distribution when the location parameter equals 0 and the scale parameter equals 1, 2, 3, and 4.