distr6 (version 1.3.6)

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.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Dirichlet$new(params = c(1, 1), decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
params	numeric	vector of concentration parameters.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Dirichlet distribution is parameterised with params as a vector of positive numerics. The parameter K is automatically calculated by counting the length of the params vector, once constructed this cannot be changed.

Public Variables

Variable	Return
name	Name of distribution.
short_name	Id of distribution.
description	Brief description of distribution.

Public Methods

Accessor Methods	Link
decorators	decorators
traits	traits
valueSupport	valueSupport
variateForm	variateForm
type	type
properties	properties
support	support
symmetry	symmetry
sup	sup
inf	inf
dmax	dmax
dmin	dmin
skewnessType	skewnessType
kurtosisType	kurtosisType

Statistical Methods Link pdf(x1, ..., log = FALSE, simplify = TRUE) pdf cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) cdf quantile(p, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) quantile.Distribution rand(n, simplify = TRUE) rand mean() mean.Distribution variance() variance stdev() stdev prec() prec cor() cor skewness() skewness kurtosis(excess = TRUE) kurtosis entropy(base = 2) entropy mgf(t) mgf cf(t) cf pgf(z) pgf median() median.Distribution iqr() iqr mode(which = "all") mode

Parameter Methods Link parameters(id) parameters getParameterValue(id, error = "warn") getParameterValue setParameterValue(..., lst = NULL, error = "warn") setParameterValue

Validation Methods Link liesInSupport(x, all = TRUE, bound = FALSE) liesInSupport liesInType(x, all = TRUE, bound = FALSE) liesInType

Representation Methods Link strprint(n = 2) strprint print(n = 2) print summary(full = T) summary.Distribution

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.

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

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

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

listDistributions for all available distributions. Beta for the Beta distribution. CoreStatistics for numerical results. FunctionImputation to numerically impute d/p/q/r.

Examples

# NOT RUN {
# Different parameterisations
x <- Dirichlet$new(params = c(2,5,6))

# Update parameters
x$setParameterValue(params = c(3, 2, 3))
# 'K' parameter is automatically calculated
x$parameters()
# }
# NOT RUN {
# This errors as less than three parameters supplied
x$setParameterValue(params = c(1, 2))
# }
# NOT RUN {
# d/p/q/r
# Note the difference from R stats
x$pdf(0.1, 0.4, 0.5)
# This allows vectorisation:
x$pdf(c(0.3, 0.2), c(0.6, 0.9), c(0.9,0.1))
x$rand(4)

# Statistics
x$mean()
x$variance()

summary(x)

# }