Degenerate: Degenerate Distribution Class In distr6: The Complete R6 Probability Distributions Interface

Description

Mathematical and statistical functions for the Degenerate distribution, which is commonly used to model deterministic events or as a representation of the delta, or Heaviside, function.

Details

The Degenerate distribution parameterised with mean, μ is defined by the pmf,

f(x) = 1, if x = μ

f(x) = 0, if x != μ

for μ ε R.

Value

Returns an R6 object inheriting from class SDistribution.

Distribution support

The distribution is supported on {μ}.

Degen(mean = 0)

N/A

Also known as

Also known as the Dirac distribution.

Super classes

`distr6::Distribution` -> `distr6::SDistribution` -> `Degenerate`

Public fields

`name`

Full name of distribution.

`short_name`

Short name of distribution for printing.

`description`

Brief description of the distribution.

Active bindings

`properties`

Returns distribution properties, including skewness type and symmetry.

Methods

Public methods

Inherited methods

Method `new()`

Creates a new instance of this R6 class.

Usage
`Degenerate\$new(mean = NULL, decorators = NULL)`
Arguments
`mean`

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

`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
`Degenerate\$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
`Degenerate\$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
`Degenerate\$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
`Degenerate\$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
`Degenerate\$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
`Degenerate\$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
`Degenerate\$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
`Degenerate\$cf(t, ...)`
Arguments
`t`

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

`...`

Unused.

Method `clone()`

The objects of this class are cloneable with this method.

Usage
`Degenerate\$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.

Other discrete distributions: `Bernoulli`, `Binomial`, `Categorical`, `DiscreteUniform`, `EmpiricalMV`, `Empirical`, `Geometric`, `Hypergeometric`, `Logarithmic`, `Multinomial`, `NegativeBinomial`, `WeightedDiscrete`
Other univariate distributions: `Arcsine`, `Bernoulli`, `BetaNoncentral`, `Beta`, `Binomial`, `Categorical`, `Cauchy`, `ChiSquaredNoncentral`, `ChiSquared`, `DiscreteUniform`, `Empirical`, `Erlang`, `Exponential`, `FDistributionNoncentral`, `FDistribution`, `Frechet`, `Gamma`, `Geometric`, `Gompertz`, `Gumbel`, `Hypergeometric`, `InverseGamma`, `Laplace`, `Logarithmic`, `Logistic`, `Loglogistic`, `Lognormal`, `NegativeBinomial`, `Normal`, `Pareto`, `Poisson`, `Rayleigh`, `ShiftedLoglogistic`, `StudentTNoncentral`, `StudentT`, `Triangular`, `Uniform`, `Wald`, `Weibull`, `WeightedDiscrete`