# Laplace: Laplace Distribution Class In distr6: The Complete R6 Probability Distributions Interface

 Laplace R Documentation

## Laplace Distribution Class

### Description

Mathematical and statistical functions for the Laplace distribution, which is commonly used in signal processing and finance.

### Details

The Laplace distribution parameterised with mean, μ, and scale, β, is defined by the pdf,

f(x) = exp(-|x-μ|/β)/(2β)

for μ ε R and β > 0.

### Value

Returns an R6 object inheriting from class SDistribution.

### Distribution support

The distribution is supported on the Reals.

### Default Parameterisation

Lap(mean = 0, scale = 1)

N/A

N/A

### Super classes

distr6::Distribution -> distr6::SDistribution -> Laplace

### Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

packages

Packages required to be installed in order to construct the distribution.

### Methods

#### Public methods

Inherited methods

#### Method new()

Creates a new instance of this R6 class.

##### Usage
Laplace\$new(mean = NULL, scale = NULL, var = NULL, decorators = NULL)
##### Arguments
mean

(numeric(1))
Mean of the distribution, defined on the Reals.

scale

(numeric(1))
Scale parameter, defined on the positive Reals.

var

(numeric(1))
Variance of the distribution, defined on the positive Reals. var = 2*scale^2. If var is provided then scale is ignored.

decorators

(character())
Decorators to add to the distribution during construction.

#### Method mean()

The arithmetic mean of a (discrete) probability distribution X is the expectation

E_X(X) = ∑ p_X(x)*x

with an integration analogue for continuous distributions.

##### Usage
Laplace\$mean(...)
...

Unused.

#### Method mode()

The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).

##### Usage
Laplace\$mode(which = "all")
##### Arguments
which

(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies which mode to return.

#### Method variance()

The variance of a distribution is defined by the formula

var_X = E[X^2] - E[X]^2

where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

##### Usage
Laplace\$variance(...)
...

Unused.

#### Method skewness()

The skewness of a distribution is defined by the third standardised moment,

sk_X = E_X[((x - μ)/σ)^3]

where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution.

##### Usage
Laplace\$skewness(...)
...

Unused.

#### Method kurtosis()

The kurtosis of a distribution is defined by the fourth standardised moment,

k_X = E_X[((x - μ)/σ)^4]

where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.

##### Usage
Laplace\$kurtosis(excess = TRUE, ...)
##### Arguments
excess

(logical(1))
If TRUE (default) excess kurtosis returned.

...

Unused.

#### Method entropy()

The entropy of a (discrete) distribution is defined by

- ∑ (f_X)log(f_X)

where f_X is the pdf of distribution X, with an integration analogue for continuous distributions.

##### Usage
Laplace\$entropy(base = 2, ...)
##### Arguments
base

(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)

...

Unused.

#### Method mgf()

The moment generating function is defined by

mgf_X(t) = E_X[exp(xt)]

where X is the distribution and E_X is the expectation of the distribution X.

##### Usage
Laplace\$mgf(t, ...)
##### Arguments
t

(integer(1))
t integer to evaluate function at.

...

Unused.

#### Method cf()

The characteristic function is defined by

cf_X(t) = E_X[exp(xti)]

where X is the distribution and E_X is the expectation of the distribution X.

##### Usage
Laplace\$cf(t, ...)
##### Arguments
t

(integer(1))
t integer to evaluate function at.

...

Unused.

#### Method pgf()

The probability generating function is defined by

pgf_X(z) = E_X[exp(z^x)]

where X is the distribution and E_X is the expectation of the distribution X.

##### Usage
Laplace\$pgf(z, ...)
##### Arguments
z

(integer(1))
z integer to evaluate probability generating function at.

...

Unused.

#### Method clone()

The objects of this class are cloneable with this method.

##### Usage
Laplace\$clone(deep = FALSE)
##### Arguments
deep

Whether to make a deep clone.

### References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.