In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together along the abscissa, although the term is also sometimes used to refer to the Gumbel distribution. The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution, as is a Brownian motion evaluated at an exponentially distributed random time[citation needed]. Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution.
^ abNorton, Matthew; Khokhlov, Valentyn; Uryasev, Stan (2019). "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation" (PDF). Annals of Operations Research. 299 (1–2). Springer: 1281–1315. doi:10.1007/s10479-019-03373-1. Retrieved 2023-02-27.
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theory and statistics, the Laplacedistribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called...
probability, multivariate Laplacedistributions are extensions of the Laplacedistribution and the asymmetric Laplacedistribution to multiple variables....
asymmetric Laplacedistribution (ALD) is a continuous probability distribution which is a generalization of the Laplacedistribution. Just as the Laplace distribution...
In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function...
potential due to a given mass density distribution is a constant multiple of that density distribution. Solutions of Laplace's equation Δf = 0 are called harmonic...
log-Weibull distribution and the double exponential distribution (a term that is alternatively sometimes used to refer to the Laplacedistribution). It is...
application of exponential distribution to particle detector analysis. Laplacedistribution, or the "double exponential distribution". Relationships among...
The Johnson SU distribution The Landau distribution The Laplacedistribution The Lévy skew alpha-stable distribution or stable distribution is a family of...
{\displaystyle X} follows log-Laplacedistribution, i.e. the random variable ln ( 1 + X ) {\displaystyle \ln(1+X)} follows Laplacedistribution the p.d.f. f ( x...
the student t distribution, the skewed Cauchy distribution, the Laplacedistribution, the uniform distribution, the normal distribution, and the Cauchy...
where the kernel is either a Laplacedistribution F ( x ; 1 , λ ) {\displaystyle F(x;1,\lambda )} or a Rayleigh distribution F ( x ; 2 , λ ) {\displaystyle...
exponential distribution may refer to Laplacedistribution, or bilateral exponential distribution, consisting of two exponential distributions glued together...
are said to be leptokurtic. An example of a leptokurtic distribution is the Laplacedistribution, which has tails that asymptotically approach zero more...
the fundamental solution for the Laplace equation in the upper half-plane. It is one of the few stable distributions with a probability density function...
asymmetric Laplacedistribution is a wrapped probability distribution that results from the "wrapping" of the asymmetric Laplacedistribution around the...
identical to the probability density function of the multivariate Laplacedistribution for two and three dimensions respectively. Yukawa interaction Kamrin...
symmetric distributions. It includes all normal and Laplacedistributions, and as limiting cases it includes all continuous uniform distributions on bounded...
t-distribution, the Laplacedistribution, the hyperbolic distribution, the normal-inverse Gaussian distribution and the variance-gamma distribution. X...
geometric stable distribution is also referred to as a Linnik distribution. The Laplacedistribution and asymmetric Laplacedistribution are special cases...
Introduced by Dwork et al., this mechanism adds noise drawn from a Laplacedistribution: M L a p ( x , f , ϵ ) = f ( x ) + L a p ( μ = 0 , b = Δ f ϵ ) ,...
a Laplacedistribution. More generally, compounding a Gaussian (or normal) distribution with variance distributed according to a gamma distribution yields...
exponential, asymmetric log-Laplace, log-Laplace, power function, and the log-logistic. The beta family of distributions (B) is defined by: B ( y ; b...
Bernoulli distribution: If X has a Rademacher distribution, then X + 1 2 {\displaystyle {\frac {X+1}{2}}} has a Bernoulli(1/2) distribution. Laplace distribution:...
English as the normal distribution or Gaussian distribution. Other less common names include Gauss distribution, Laplace-Gauss distribution, the law of error...
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