CoreStatistics: Core Statistical Methods Decorator
In alan-turing-institute/distr6: The Complete R6 Probability Distributions Interface
CoreStatistics R Documentation
Core Statistical Methods Decorator
Description
This decorator adds numeric methods for missing analytic expressions in
Distributions as well as adding generalised expectation and moments functions.
Details
Decorator objects add functionality to the given Distribution object by copying methods
in the decorator environment to the chosen Distribution environment.
All methods implemented in decorators try to exploit analytical results where possible, otherwise
numerical results are used with a message.
Super class
distr6::DistributionDecorator -> CoreStatistics
Methods
Public methods
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Inherited methods
Method mgf()
Numerically estimates the moment-generating function.
Usage
CoreStatistics$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...ANY
Passed to $genExp.
Method cf()
Numerically estimates the characteristic function.
Usage
CoreStatistics$cf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...ANY
Passed to $genExp.
Method pgf()
Numerically estimates the probability-generating function.
Usage
CoreStatistics$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at.
...ANY
Passed to $genExp.
Method entropy()
Numerically estimates the entropy function.
Usage
CoreStatistics$entropy(base = 2, ...)
Arguments
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)
...ANY
Passed to $genExp.
Method skewness()
Numerically estimates the distribution skewness.
Usage
CoreStatistics$skewness(...)
Arguments
...ANY
Passed to $genExp.
Method kurtosis()
Numerically estimates the distribution kurtosis.
Usage
CoreStatistics$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...ANY
Passed to $genExp.
Method variance()
Numerically estimates the distribution variance.
Usage
CoreStatistics$variance(...)
Arguments
...ANY
Passed to $genExp.
Method kthmoment()
The kth central moment of a distribution is defined by
CM(k)_X = E_X[(x - \mu)^k]
the kth standardised moment of a distribution is defined by
SM(k)_X = \frac{CM(k)}{\sigma^k}
the kth raw moment of a distribution is defined by
RM(k)_X = E_X[x^k]
where E_X is the expectation of distribution X, \mu is the mean of the
distribution and \sigma is the standard deviation of the distribution.
Usage
CoreStatistics$kthmoment(k, type = c("central", "standard", "raw"), ...)
Arguments
kinteger(1)
The k-th moment to evaluate the distribution at.
typecharacter(1)
Type of moment to evaluate.
...ANY
Passed to $genExp.
Method genExp()
Numerically estimates E[f(X)] for some function f.
Usage
CoreStatistics$genExp(trafo = NULL, cubature = FALSE, ...)
Arguments
trafofunction()
Transformation function to define the expectation, default is distribution mean.
cubaturelogical(1)
If TRUE uses cubature::cubintegrate for approximation, otherwise integrate.
...ANY
Passed to cubature::cubintegrate.
Method mode()
Numerically estimates the distribution mode.
Usage
CoreStatistics$mode(which = "all")
Arguments
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies
which mode to return.
Method mean()
Numerically estimates the distribution mean.
Usage
CoreStatistics$mean(...)
Arguments
...ANY
Passed to $genExp.
Method clone()
The objects of this class are cloneable with this method.
Usage
CoreStatistics$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
See Also
Other decorators:
ExoticStatistics,
FunctionImputation
Examples
decorate(Exponential$new(), "CoreStatistics")
Exponential$new(decorators = "CoreStatistics")
CoreStatistics$new()$decorate(Exponential$new())
alan-turing-institute/distr6 documentation built on Feb. 26, 2024, 11 a.m.
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| CoreStatistics | R Documentation |
Core Statistical Methods Decorator
Description
This decorator adds numeric methods for missing analytic expressions in Distributions as well as adding generalised expectation and moments functions.
Details
Decorator objects add functionality to the given Distribution object by copying methods in the decorator environment to the chosen Distribution environment.
All methods implemented in decorators try to exploit analytical results where possible, otherwise numerical results are used with a message.
Super class
distr6::DistributionDecorator -> CoreStatistics
Methods
Public methods
Inherited methods
Method mgf()
Numerically estimates the moment-generating function.
Usage
CoreStatistics$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....ANY
Passed to$genExp.
Method cf()
Numerically estimates the characteristic function.
Usage
CoreStatistics$cf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....ANY
Passed to$genExp.
Method pgf()
Numerically estimates the probability-generating function.
Usage
CoreStatistics$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at....ANY
Passed to$genExp.
Method entropy()
Numerically estimates the entropy function.
Usage
CoreStatistics$entropy(base = 2, ...)
Arguments
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)...ANY
Passed to$genExp.
Method skewness()
Numerically estimates the distribution skewness.
Usage
CoreStatistics$skewness(...)
Arguments
...ANY
Passed to$genExp.
Method kurtosis()
Numerically estimates the distribution kurtosis.
Usage
CoreStatistics$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
IfTRUE(default) excess kurtosis returned....ANY
Passed to$genExp.
Method variance()
Numerically estimates the distribution variance.
Usage
CoreStatistics$variance(...)
Arguments
...ANY
Passed to$genExp.
Method kthmoment()
The kth central moment of a distribution is defined by
CM(k)_X = E_X[(x - \mu)^k]
the kth standardised moment of a distribution is defined by
SM(k)_X = \frac{CM(k)}{\sigma^k}
the kth raw moment of a distribution is defined by
RM(k)_X = E_X[x^k]
where E_X is the expectation of distribution X, \mu is the mean of the
distribution and \sigma is the standard deviation of the distribution.
Usage
CoreStatistics$kthmoment(k, type = c("central", "standard", "raw"), ...)Arguments
kinteger(1)
Thek-th moment to evaluate the distribution at.typecharacter(1)
Type of moment to evaluate....ANY
Passed to$genExp.
Method genExp()
Numerically estimates E[f(X)] for some function f.
Usage
CoreStatistics$genExp(trafo = NULL, cubature = FALSE, ...)
Arguments
trafofunction()
Transformation function to define the expectation, default is distribution mean.cubaturelogical(1)
IfTRUEuses cubature::cubintegrate for approximation, otherwise integrate....ANY
Passed to cubature::cubintegrate.
Method mode()
Numerically estimates the distribution mode.
Usage
CoreStatistics$mode(which = "all")
Arguments
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise"all"returns all modes, otherwise specifies which mode to return.
Method mean()
Numerically estimates the distribution mean.
Usage
CoreStatistics$mean(...)
Arguments
...ANY
Passed to$genExp.
Method clone()
The objects of this class are cloneable with this method.
Usage
CoreStatistics$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
See Also
Other decorators:
ExoticStatistics,
FunctionImputation
Examples
decorate(Exponential$new(), "CoreStatistics")
Exponential$new(decorators = "CoreStatistics")
CoreStatistics$new()$decorate(Exponential$new())
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