## Laplace Distribution

Also called the Double Exponential Distribution. It is the distribution of differences between two independent variates with identical Exponential Distributions (Abramowitz and Stegun 1972, p. 930).

 (1) (2)

The Moments about the Mean are related to the Moments about 0 by
 (3)

where is a Binomial Coefficient, so
 (4)

where is the Floor Function and is the Gamma Function.

The Moments can also be computed using the Characteristic Function,

 (5)

Using the Fourier Transform of the Exponential Function
 (6)

gives
 (7)

The Moments are therefore
 (8)

The Mean, Variance, Skewness, and Kurtosis are
 (9) (10) (11) (12)

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.