Learn R Programming

distr6 (version 1.6.9)

Dirichlet: Dirichlet Distribution Class

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.

Arguments

Value

Returns an R6 object inheriting from class SDistribution.

Distribution support

The distribution is supported on \(x_i \ \epsilon \ (0,1), \sum x_i = 1\).

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

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 $$E_X(X) = \sum p_X(x)*x$$ 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 $$- \sum (f_X)log(f_X)$$ 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.

Details

The Dirichlet distribution parameterised with concentration parameters, \(\alpha_1,...,\alpha_k\), is defined by the pdf, $$f(x_1,...,x_k) = (\prod \Gamma(\alpha_i))/(\Gamma(\sum \alpha_i))\prod(x_i^{\alpha_i - 1})$$ for \(\alpha = \alpha_1,...,\alpha_k; \alpha > 0\), where \(\Gamma\) is the gamma function.

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

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

Run this code
# NOT RUN {
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))
# }

Run the code above in your browser using DataLab