Log-Laplace distribution
Probability density function
Probability density functions for Log-Laplace distributions with varying parameters and .
Cumulative distribution function
Cumulative distribution functions for Log-Laplace distributions with varying parameters and .

In probability theory and statistics, the log-Laplace distribution is the probability distribution of a random variable whose logarithm has a Laplace distribution. If X has a Laplace distribution with parameters μ and b, then Y = eX has a log-Laplace distribution. The distributional properties can be derived from the Laplace distribution.


A random variable has a log-Laplace(μ, b) distribution if its probability density function is:[1]

The cumulative distribution function for Y when y > 0, is


Versions of the log-Laplace distribution based on an asymmetric Laplace distribution also exist.[2] Depending on the parameters, including asymmetry, the log-Laplace may or may not have a finite mean and a finite variance.[2]


  1. ^ Lindsey, J.K. (2004). Statistical analysis of stochastic processes in time. Cambridge University Press. p. 33. ISBN 978-0-521-83741-5.
  2. ^ a b Kozubowski, T.J. & Podgorski, K. "A Log-Laplace Growth Rate Model" (PDF). University of Nevada-Reno. p. 4. Archived from the original (PDF) on 2012-04-15. Retrieved 2011-10-21.