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Log-Laplace distribution 
Summary
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.
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Probability density function  Probability density functions for Log-Laplace distributions with varying parameters and . | |||
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Cumulative distribution function  Cumulative distribution functions for Log-Laplace distributions with varying parameters and . |
Characterization edit
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
![{\displaystyle F(y)=0.5\,[1+\operatorname {sgn}(\ln(y)-\mu )\,(1-\exp(-|\ln(y)-\mu |/b))].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb52418a310d1f690cf40a471db17e51c0917409)
Generalization edit
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]
References edit
- ^ Lindsey, J.K. (2004). Statistical analysis of stochastic processes in time. Cambridge University Press. p. 33. ISBN 978-0-521-83741-5.
- ^ 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.