Dirichlet: Dirichlet Distribution Class
In distr6: The Complete R6 Probability Distributions Interface
Dirichlet R Documentation
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.
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
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.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
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Inherited methods
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Method new()
Creates a new instance of this R6 class.
Usage
Dirichlet$new(params = NULL, decorators = NULL)
Arguments
paramsnumeric()
Vector of concentration parameters of the distribution defined on the positive Reals.
decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
Usage
Dirichlet$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
deepWhether 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
d <- Dirichlet$new(params = c(2, 5, 6))
d$pdf(0.1, 0.4, 0.5)
d$pdf(c(0.3, 0.2), c(0.6, 0.9), c(0.9, 0.1))
distr6 documentation built on March 28, 2022, 1:05 a.m.
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| Dirichlet | R Documentation |
Dirichlet Distribution Class
Description
Mathematical and statistical functions for the Dirichlet distribution, which is commonly used as a prior in Bayesian modelling and is multivariate generalisation of the Beta distribution.
Details
The Dirichlet distribution parameterised with concentration parameters, α_1,...,α_k, is defined by the pdf,
f(x_1,...,x_k) = (∏ Γ(α_i))/(Γ(∑ α_i))∏(x_i^{α_i - 1})
for α = α_1,...,α_k; α > 0, where Γ is the gamma function.
Sampling is performed via sampling independent Gamma distributions and normalising the samples (Devroye, 1986).
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on x_i ε (0,1), ∑ x_i = 1.
Default Parameterisation
Diri(params = c(1, 1))
Omitted Methods
cdf and quantile
are
omitted as no closed form analytic expression could be found, decorate with FunctionImputation for a numerical imputation.
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> Dirichlet
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages required to be installed in order to construct the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
Inherited methods
Method new()
Creates a new instance of this R6 class.
Usage
Dirichlet$new(params = NULL, decorators = NULL)
Arguments
paramsnumeric()
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))
IfFALSE(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$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
References
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
Devroye, Luc (1986). Non-Uniform Random Variate Generation. Springer-Verlag. ISBN 0-387-96305-7.
See Also
Other continuous distributions:
Arcsine,
BetaNoncentral,
Beta,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Gompertz,
Gumbel,
InverseGamma,
Laplace,
Logistic,
Loglogistic,
Lognormal,
MultivariateNormal,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
Other multivariate distributions:
EmpiricalMV,
Multinomial,
MultivariateNormal
Examples
d <- Dirichlet$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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