Scale relativity

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

Probability density function

A random variable has a Laplace(μ, b) distribution if its probability density function is:

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

$={\frac {1}{2bx}}\left\{{\begin{matrix}\exp \left(-{\frac {\mu -\ln x}{b}}\right)&{\mbox{if }}x<\mu \\[8pt]\exp \left(-{\frac {\ln x-\mu }{b}}\right)&{\mbox{if }}x\geq \mu \end{matrix}}\right.$

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

$F(y)=0.5\,[1+\operatorname {sgn}(\log(y)-\mu )\,(1-\exp(-|\log(y)-\mu |/b))].$

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.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

55 yrs old Metal Polisher Records from Gypsumville, has interests which include owning an antique car, summoners war hack and spelunkering. Gets immense motivation from life by going to places such as Villa Adriana (Tivoli).

my web site - summoners war hack no survey ios Template:Probability-stub