# Laplace distribution

**Laplacedouble exponentialLaplace distributedLaplace prior distributionsLaplace(''μ'', ''b'')Laplace(0, 1)Laplaciantwo-sided decaying exponential function**

In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.wikipedia

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### Gumbel distribution

**GumbelLog-Weibull distributiondouble exponential distribution**

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 back-to-back, although the term is also sometimes used to refer to the Gumbel distribution.

It is also known as the log-Weibull distribution and the double exponential distribution (a term that is alternatively sometimes used to refer to the Laplace distribution).

### Exponential distribution

**exponentialexponentially distributedexponentially**

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 back-to-back, although the term is also sometimes used to refer to the Gumbel distribution.

### Variance gamma process

**Laplace motionVariance Gammavariance gamma model**

Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution.

The increments are independent and follow a Variance-gamma distribution, which is a generalization of the Laplace distribution.

### Generalized normal distribution

**exponential power distributionGeneralized Gaussian distributionGED**

It includes all normal and Laplace distributions, and as limiting cases it includes all continuous uniform distributions on bounded intervals of the real line.

### Least absolute deviations

**Least absolute deviationLeast absolute errorsLAD**

:(revealing a link between the Laplace distribution and least absolute deviations).

The least absolute deviations estimate also arises as the maximum likelihood estimate if the errors have a Laplace distribution.

### Geometric stable distribution

**Linnik distribution**

The Laplace distribution and asymmetric Laplace distribution are special cases of the geometric stable distribution.

### Multivariate Laplace distribution

**Symmetric multivariate Laplace distribution**

In the mathematical theory of probability, multivariate Laplace distributions are extensions of the Laplace distribution and the asymmetric Laplace distribution to multiple variables.

### Chi-squared distribution

**chi-squaredchi-square distributionchi square distribution**

### Characteristic function (probability theory)

**characteristic functioncharacteristic functionscharacteristic function:**

One way to show this is by using the characteristic function approach.

### Differential privacy

**differentially privateprivacy-preserving**

*The addition of noise drawn from a Laplacian distribution, with scaling parameter appropriate to a function's sensitivity, to the output of a statistical database query is the most common means to provide differential privacy in statistical databases.

The Laplace mechanism adds Laplace noise (i.e. noise from the Laplace distribution, which can be expressed by probability density function, which has mean zero and standard deviation ).

### F-distribution

**F distributionF''-distributionF'' distribution**

### CumFreq

The following probability distributions are included: normal, lognormal, logistic, loglogistic, exponential, Cauchy, Fréchet, Gumbel, Pareto, Weibull, Generalized extreme value distribution, Laplace distribution, Burr distribution (Dagum mirrored), Dagum distribution (Burr mirrored), Gompertz distribution, Student distribution and other.

### Besov measure

In mathematics — specifically, in the fields of probability theory and inverse problems — Besov measures and associated Besov-distributed random variables are generalisations of the notions of Gaussian measures and random variables, Laplace distributions, and other classical distributions.

### Rademacher distribution

**Rademacher random variablesRademacher**

### Lasso (statistics)

**LASSOLasso methodLeast Absolute Shrinkage and Selection Operator**

Just as ridge regression can be interpreted as linear regression for which the coefficients have been assigned normal prior distributions, lasso can be interpreted as linear regression for which the coefficients have Laplace prior distributions.

### Log-Laplace distribution

**log-Laplace**

In probability theory and statistics, the log-Laplace distribution is the probability distribution of a random variable whose logarithm has a Laplace distribution.

### Probability theory

**theory of probabilityprobabilityprobability theorist**

In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.

### Statistics

**statisticalstatistical analysisstatistician**

In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.

### Probability distribution

**distributioncontinuous probability distributiondiscrete probability distribution**

In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.

### Pierre-Simon Laplace

**LaplacePierre Simon LaplacePierre-Simon de Laplace**

### Brownian motion

**BrownianBrownian movementBrownian particle**

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.

### Random variable

**random variablesrandom variationrandom**

A random variable has a distribution if its probability density function is

### Probability density function

**probability densitydensity functiondensity**

A random variable has a distribution if its probability density function is

### Location parameter

**locationlocation modellocation parameters**

Here, \mu is a location parameter and b > 0, which is sometimes referred to as the diversity, is a scale parameter.

### Scale parameter

**scalerate parameterestimation**

Here, \mu is a location parameter and b > 0, which is sometimes referred to as the diversity, is a scale parameter.