Dirichlet Distribution Class
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.
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).
Returns an R6 object inheriting from class SDistribution.
The distribution is supported on x_i ε (0,1), ∑ x_i = 1.
Diri(params = c(1, 1))
cdf and quantile
are
omitted as no closed form analytic expression could be found, decorate with FunctionImputation for a numerical imputation.
N/A
distr6::Distribution -> distr6::SDistribution -> Dirichlet
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages required to be installed in order to construct the distribution.
new()
Creates a new instance of this R6 class.
Dirichlet$new(params = NULL, decorators = NULL)
paramsnumeric()
Vector of concentration parameters of the distribution defined on the positive Reals.
decorators(character())
Decorators to add to the distribution during construction.
mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
Dirichlet$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).
Dirichlet$mode(which = "all")
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies
which mode to return.
variance()
The variance of a distribution is defined by the formula
var_X = E[X^2] - E[X]^2
where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.
Dirichlet$variance(...)
...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.
Dirichlet$entropy(base = 2, ...)
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)
...Unused.
pgf()
The probability generating function is defined by
pgf_X(z) = E_X[exp(z^x)]
where X is the distribution and E_X is the expectation of the distribution X.
Dirichlet$pgf(z, ...)
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
setParameterValue()
Sets the value(s) of the given parameter(s).
Dirichlet$setParameterValue( ..., lst = NULL, error = "warn", resolveConflicts = FALSE )
...ANY
Named arguments of parameters to set values for. See examples.
lst(list(1))
Alternative argument for passing parameters. List names should be parameter names and list values
are the new values to set.
error(character(1))
If "warn" then returns a warning on error, otherwise breaks if "stop".
resolveConflicts(logical(1))
If FALSE (default) throws error if conflicting parameterisations are provided, otherwise
automatically resolves them by removing all conflicting parameters.
clone()
The objects of this class are cloneable with this method.
Dirichlet$clone(deep = FALSE)
deepWhether to make a deep clone.
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.
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
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))
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