Dirichlet: Dirichlet Distribution Class

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

Description

Mathematical and statistical functions for the Dirichlet distribution, which is commonly used as a prior in Bayesian modelling and is multivariate generalisation of the Beta distribution.

Details

The Dirichlet distribution parameterised with concentration parameters, α_1,...,α_k, is defined by the pdf,

f(x_1,...,x_k) = (∏ Γ(α_i))/(Γ(∑ α_i))∏(x_i^{α_i - 1})

for α = α_1,...,α_k; α > 0, where Γ is the gamma function.

Sampling is performed via sampling independent Gamma distributions and normalising the samples (Devroye, 1986).

Value

Returns an R6 object inheriting from class SDistribution.

Distribution support

The distribution is supported on x_i ε (0,1), ∑ x_i = 1.

Default Parameterisation

Diri(params = c(1, 1))

Omitted Methods

cdf and quantile are omitted as no closed form analytic expression could be found, decorate with FunctionImputation for a numerical imputation.

Also known as

N/A

Super classes

distr6::Distribution -> distr6::SDistribution -> Dirichlet

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.

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
Dirichlet$new(params = NULL, decorators = NULL)
Arguments
params

numeric()
Vector of concentration parameters of the distribution defined on the positive 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
Dirichlet$mean(...)
Arguments
...

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
Dirichlet$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
Dirichlet$variance(...)
Arguments
...

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
Dirichlet$entropy(base = 2, ...)
Arguments
base

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

...

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
Dirichlet$pgf(z, ...)
Arguments
z

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

...

Unused.


Method setParameterValue()

Sets the value(s) of the given parameter(s).

Usage
Dirichlet$setParameterValue(
  ...,
  lst = list(...),
  error = "warn",
  resolveConflicts = FALSE
)
Arguments
...

ANY
Named arguments of parameters to set values for. See examples.

lst

(list(1))
Alternative argument for passing parameters. List names should be parameter names and list values are the new values to set.

error

(character(1))
If "warn" then returns a warning on error, otherwise breaks if "stop".

resolveConflicts

(logical(1))
If FALSE (default) throws error if conflicting parameterisations are provided, otherwise automatically resolves them by removing all conflicting parameters.


Method clone()

The objects of this class are cloneable with this method.

Usage
Dirichlet$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.

Devroye, Luc (1986). Non-Uniform Random Variate Generation. Springer-Verlag. ISBN 0-387-96305-7.

See Also

Other continuous distributions: Arcsine, BetaNoncentral, Beta, Cauchy, ChiSquaredNoncentral, ChiSquared, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gamma, Gompertz, Gumbel, InverseGamma, Laplace, Logistic, Loglogistic, Lognormal, MultivariateNormal, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull

Other multivariate distributions: EmpiricalMV, Multinomial, MultivariateNormal

Examples

1
2
3
d <- Dirichlet$new(params = c(2, 5, 6))
d$pdf(0.1, 0.4, 0.5)
d$pdf(c(0.3, 0.2), c(0.6, 0.9), c(0.9, 0.1))

distr6 documentation built on Sept. 6, 2021, 9:10 a.m.