log-Laplace distribution

{{Infobox probability distribution

| name = Log-Laplace distribution

| type = density

| pdf_image = Log-Laplace PDF.png

| pdf_caption = Probability density functions for Log-Laplace distributions with varying parameters $\mu$ and $b$ .

| cdf_image = Log-Laplace CDF.png

| cdf_caption = Cumulative distribution functions for Log-Laplace distributions with varying parameters $\mu$ and $b$ .

}}

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 = e^X has a log-Laplace distribution. The distributional properties can be derived from the Laplace distribution.

Characterization

A random variable has a log-Laplace(μ, b) distribution if its probability density function is:{{cite book|title=Statistical analysis of stochastic processes in time|author=Lindsey, J.K.|page=33|year=2004|publisher=Cambridge University Press|isbn=978-0-521-83741-5}}

: $f(x|\mu,b) = \frac{1}{2bx} \exp \left( -\frac$

\ln x-\mu

{b} \right)

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

: $F(y) = 0.5\,[1 + \sgn(\ln(y)-\mu)\,(1-\exp(-|\ln(y)-\mu|/b))].$

Generalization

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.{{cite web|title=A Log-Laplace Growth Rate Model|url=http://wolfweb.unr.edu/homepage/tkozubow/0_logs.pdf|author1=Kozubowski, T.J.|author2=Podgorski, K.|name-list-style=amp|page=4|publisher=University of Nevada-Reno|access-date=2011-10-21|archive-url=https://web.archive.org/web/20120415102754/http://wolfweb.unr.edu/homepage/tkozubow/0_logs.pdf|archive-date=2012-04-15|url-status=dead}}

References

Category:Continuous distributions

Category:Probability distributions with non-finite variance

Category:Non-Newtonian calculus