Description Details Value Distribution support Default Parameterisation Omitted Methods Also known as Super classes Public fields Methods References See Also

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

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*.

Returns an R6 object inheriting from class SDistribution.

The distribution is supported on the Reals.

Lap(mean = 0, scale = 1)

N/A

N/A

`distr6::Distribution`

-> `distr6::SDistribution`

-> `Laplace`

`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.

`new()`

Creates a new instance of this R6 class.

Laplace$new(mean = NULL, scale = NULL, var = NULL, decorators = NULL)

`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.

`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.

Laplace$mean(...)

`...`

Unused.

`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).

Laplace$mode(which = "all")

`which`

`(character(1) | numeric(1)`

Ignored if distribution is unimodal. Otherwise`"all"`

returns all modes, otherwise specifies which mode to return.

`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.

Laplace$variance(...)

`...`

Unused.

`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.

Laplace$skewness(...)

`...`

Unused.

`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.

Laplace$kurtosis(excess = TRUE, ...)

`excess`

`(logical(1))`

If`TRUE`

(default) excess kurtosis returned.`...`

Unused.

`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.

Laplace$entropy(base = 2, ...)

`base`

`(integer(1))`

Base of the entropy logarithm, default = 2 (Shannon entropy)`...`

Unused.

`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.

Laplace$mgf(t, ...)

`t`

`(integer(1))`

t integer to evaluate function at.`...`

Unused.

`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.

Laplace$cf(t, ...)

`t`

`(integer(1))`

t integer to evaluate function at.`...`

Unused.

`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.

Laplace$pgf(z, ...)

`z`

`(integer(1))`

z integer to evaluate probability generating function at.`...`

Unused.

`clone()`

The objects of this class are cloneable with this method.

Laplace$clone(deep = FALSE)

`deep`

Whether to make a deep clone.

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

Other continuous distributions:
`Arcsine`

,
`BetaNoncentral`

,
`Beta`

,
`Cauchy`

,
`ChiSquaredNoncentral`

,
`ChiSquared`

,
`Dirichlet`

,
`Erlang`

,
`Exponential`

,
`FDistributionNoncentral`

,
`FDistribution`

,
`Frechet`

,
`Gamma`

,
`Gompertz`

,
`Gumbel`

,
`InverseGamma`

,
`Logistic`

,
`Loglogistic`

,
`Lognormal`

,
`MultivariateNormal`

,
`Normal`

,
`Pareto`

,
`Poisson`

,
`Rayleigh`

,
`ShiftedLoglogistic`

,
`StudentTNoncentral`

,
`StudentT`

,
`Triangular`

,
`Uniform`

,
`Wald`

,
`Weibull`

Other univariate distributions:
`Arcsine`

,
`Bernoulli`

,
`BetaNoncentral`

,
`Beta`

,
`Binomial`

,
`Categorical`

,
`Cauchy`

,
`ChiSquaredNoncentral`

,
`ChiSquared`

,
`Degenerate`

,
`DiscreteUniform`

,
`Empirical`

,
`Erlang`

,
`Exponential`

,
`FDistributionNoncentral`

,
`FDistribution`

,
`Frechet`

,
`Gamma`

,
`Geometric`

,
`Gompertz`

,
`Gumbel`

,
`Hypergeometric`

,
`InverseGamma`

,
`Logarithmic`

,
`Logistic`

,
`Loglogistic`

,
`Lognormal`

,
`NegativeBinomial`

,
`Normal`

,
`Pareto`

,
`Poisson`

,
`Rayleigh`

,
`ShiftedLoglogistic`

,
`StudentTNoncentral`

,
`StudentT`

,
`Triangular`

,
`Uniform`

,
`Wald`

,
`Weibull`

,
`WeightedDiscrete`

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