| Log-Laplace distribution | |
| Type: | density |
| Pdf Image: | Log-Laplace PDF.png |
| Pdf Caption: | Probability density functions for Log-Laplace distributions with varying parameters \mu b |
| Cdf Image: | Log-Laplace CDF.png |
| Cdf Caption: | Cumulative distribution functions for Log-Laplace distributions with varying parameters \mu b |
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]
f(x|\mu,b)=
| 1 | |
| 2bx |
\exp\left(-
| |lnx-\mu| | |
| b |
\right)
The cumulative distribution function for Y when y > 0, is
F(y)=0.5[1+sgn(ln(y)-\mu)(1-\exp(-|ln(y)-\mu|/b))].
Versions of the log-Laplace distribution based on an asymmetric Laplace distribution also exist. Depending on the parameters, including asymmetry, the log-Laplace may or may not have a finite mean and a finite variance.[2]