MixtureDistribution: Mixture Distribution Wrapper
In distr6: The Complete R6 Probability Distributions Interface
MixtureDistribution R Documentation
Mixture Distribution Wrapper
Description
Wrapper used to construct a mixture of two or more distributions.
Details
A mixture distribution is defined by
F_P(x) = w_1 F_X1(x) * ... * w_n F_XN(x)
#nolint
where F_P is the cdf of the mixture distribution, X1,...,XN are
independent distributions, and w1,...,wN are weights for the mixture.
Super classes
distr6::Distribution -> distr6::DistributionWrapper -> distr6::VectorDistribution -> MixtureDistribution
Methods
Public methods
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Inherited methods
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Method new()
Creates a new instance of this R6 class.
Usage
MixtureDistribution$new(
distlist = NULL,
weights = "uniform",
distribution = NULL,
params = NULL,
shared_params = NULL,
name = NULL,
short_name = NULL,
decorators = NULL,
vecdist = NULL,
ids = NULL
)
Arguments
distlist(list())
List of Distributions.
weights(character(1)|numeric())
Weights to use in the resulting mixture. If all distributions are weighted equally then
"uniform" provides a much faster implementation, otherwise a vector of length equal
to the number of wrapped distributions, this is automatically scaled internally.
distribution(character(1))
Should be supplied with params and optionally shared_params as an alternative to distlist.
Much faster implementation when only one class of distribution is being wrapped. distribution
is the full name of one of the distributions in listDistributions(), or "Distribution" if
constructing custom distributions. See examples in VectorDistribution.
params(list()|data.frame())
Parameters in the individual distributions for use with distribution. Can be supplied as a list,
where each element is the list of parameters to set in the distribution, or as an object
coercable to data.frame, where each column is a parameter and each row is a distribution.
See examples in VectorDistribution.
shared_params(list())
If any parameters are shared when using the distribution constructor, this provides a much faster
implementation to list and query them together. See examples in VectorDistribution.
name(character(1))
Optional name of wrapped distribution.
short_name(character(1))
Optional short name/ID of wrapped distribution.
decorators(character())
Decorators to add to the distribution during construction.
vecdistVectorDistribution
Alternative constructor to directly create this object from an object inheriting from
VectorDistribution.
ids(character())
Optional ids for wrapped distributions in vector, should be unique and of same length as
the number of distributions.
Examples
MixtureDistribution$new(list(Binomial$new(prob = 0.5, size = 10), Binomial$new()),
weights = c(0.2, 0.8)
)
Method strprint()
Printable string representation of the MixtureDistribution. Primarily used internally.
Usage
MixtureDistribution$strprint(n = 10)
Arguments
n(integer(1))
Number of distributions to include when printing.
Method pdf()
Probability density function of the mixture distribution. Computed by
f_M(x) = ∑_i (f_i)(x)*w_i
where w_i is the vector of weights and f_i are the pdfs of the wrapped
distributions.
Note that as this class inherits from VectorDistribution, it is possible to evaluate
the distributions at different points, but that this is not the usual use-case for
mixture distributions.
Usage
MixtureDistribution$pdf(..., log = FALSE, simplify = TRUE, data = NULL)
Arguments
...(numeric())
Points to evaluate the function at Arguments do not need
to be named. The length of each argument corresponds to the number of points to evaluate,
the number of arguments corresponds to the number of variables in the distribution.
See examples.
log(logical(1))
If TRUE returns the logarithm of the probabilities. Default is FALSE.
simplifylogical(1)
If TRUE (default) simplifies the return if possible to a numeric, otherwise returns a
data.table::data.table.
dataarray
Alternative method to specify points to evaluate. If univariate then rows correspond with number
of points to evaluate and columns correspond with number of variables to evaluate. In the special
case of VectorDistributions of multivariate distributions, then the third dimension corresponds
to the distribution in the vector to evaluate.
Examples
m <- MixtureDistribution$new(list(Binomial$new(prob = 0.5, size = 10), Binomial$new()),
weights = c(0.2, 0.8)
)
m$pdf(1:5)
m$pdf(1)
# also possible but unlikely to be used
m$pdf(1, 2)
Method cdf()
Cumulative distribution function of the mixture distribution. Computed by
F_M(x) = ∑_i (F_i)(x)*w_i
where w_i is the vector of weights and F_i are the cdfs of the wrapped
distributions.
Usage
MixtureDistribution$cdf(
...,
lower.tail = TRUE,
log.p = FALSE,
simplify = TRUE,
data = NULL
)
Arguments
...(numeric())
Points to evaluate the function at Arguments do not need
to be named. The length of each argument corresponds to the number of points to evaluate,
the number of arguments corresponds to the number of variables in the distribution.
See examples.
@examples
m <- MixtureDistribution$new(list(Binomial$new(prob = 0.5, size = 10), Binomial$new()),
weights = c(0.2, 0.8)
)
m$cdf(1:5)
lower.tail(logical(1))
If TRUE (default), probabilities are X <= x, otherwise, P(X > x).
log.p(logical(1))
If TRUE returns the logarithm of the probabilities. Default is FALSE.
simplifylogical(1)
If TRUE (default) simplifies the return if possible to a numeric, otherwise returns a
data.table::data.table.
dataarray
Alternative method to specify points to evaluate. If univariate then rows correspond with number
of points to evaluate and columns correspond with number of variables to evaluate. In the special
case of VectorDistributions of multivariate distributions, then the third dimension corresponds
to the distribution in the vector to evaluate.
Method quantile()
The quantile function is not implemented for mixture distributions.
Usage
MixtureDistribution$quantile(
...,
lower.tail = TRUE,
log.p = FALSE,
simplify = TRUE,
data = NULL
)
Arguments
...(numeric())
Points to evaluate the function at Arguments do not need
to be named. The length of each argument corresponds to the number of points to evaluate,
the number of arguments corresponds to the number of variables in the distribution.
See examples.
lower.tail(logical(1))
If TRUE (default), probabilities are X <= x, otherwise, P(X > x).
log.p(logical(1))
If TRUE returns the logarithm of the probabilities. Default is FALSE.
simplifylogical(1)
If TRUE (default) simplifies the return if possible to a numeric, otherwise returns a
data.table::data.table.
dataarray
Alternative method to specify points to evaluate. If univariate then rows correspond with number
of points to evaluate and columns correspond with number of variables to evaluate. In the special
case of VectorDistributions of multivariate distributions, then the third dimension corresponds
to the distribution in the vector to evaluate.
Method rand()
Simulation function for mixture distributions. Samples are drawn from a mixture by first
sampling Multinomial(probs = weights, size = n), then sampling each distribution according
to the samples from the Multinomial, and finally randomly permuting these draws.
Usage
MixtureDistribution$rand(n, simplify = TRUE)
Arguments
n(numeric(1))
Number of points to simulate from the distribution. If length greater than 1, then
n <- length(n),
simplifylogical(1)
If TRUE (default) simplifies the return if possible to a numeric, otherwise returns a
data.table::data.table.
Examples
m <- MixtureDistribution$new(distribution = "Normal",
params = data.frame(mean = 1:2, sd = 1))
m$rand(5)
Method clone()
The objects of this class are cloneable with this method.
Usage
MixtureDistribution$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
See Also
Other wrappers:
Convolution,
DistributionWrapper,
HuberizedDistribution,
ProductDistribution,
TruncatedDistribution,
VectorDistribution
Examples
## ------------------------------------------------
## Method `MixtureDistribution$new`
## ------------------------------------------------
MixtureDistribution$new(list(Binomial$new(prob = 0.5, size = 10), Binomial$new()),
weights = c(0.2, 0.8)
)
## ------------------------------------------------
## Method `MixtureDistribution$pdf`
## ------------------------------------------------
m <- MixtureDistribution$new(list(Binomial$new(prob = 0.5, size = 10), Binomial$new()),
weights = c(0.2, 0.8)
)
m$pdf(1:5)
m$pdf(1)
# also possible but unlikely to be used
m$pdf(1, 2)
## ------------------------------------------------
## Method `MixtureDistribution$rand`
## ------------------------------------------------
m <- MixtureDistribution$new(distribution = "Normal",
params = data.frame(mean = 1:2, sd = 1))
m$rand(5)
distr6 documentation built on March 28, 2022, 1:05 a.m.
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| MixtureDistribution | R Documentation |
Mixture Distribution Wrapper
Description
Wrapper used to construct a mixture of two or more distributions.
Details
A mixture distribution is defined by
F_P(x) = w_1 F_X1(x) * ... * w_n F_XN(x)
#nolint where F_P is the cdf of the mixture distribution, X1,...,XN are independent distributions, and w1,...,wN are weights for the mixture.
Super classes
distr6::Distribution -> distr6::DistributionWrapper -> distr6::VectorDistribution -> MixtureDistribution
Methods
Public methods
Inherited methods
Method new()
Creates a new instance of this R6 class.
Usage
MixtureDistribution$new( distlist = NULL, weights = "uniform", distribution = NULL, params = NULL, shared_params = NULL, name = NULL, short_name = NULL, decorators = NULL, vecdist = NULL, ids = NULL )
Arguments
distlist(list())
List of Distributions.weights(character(1)|numeric())
Weights to use in the resulting mixture. If all distributions are weighted equally then"uniform"provides a much faster implementation, otherwise a vector of length equal to the number of wrapped distributions, this is automatically scaled internally.distribution(character(1))
Should be supplied withparamsand optionallyshared_paramsas an alternative todistlist. Much faster implementation when only one class of distribution is being wrapped.distributionis the full name of one of the distributions inlistDistributions(), or"Distribution"if constructing custom distributions. See examples in VectorDistribution.params(list()|data.frame())
Parameters in the individual distributions for use withdistribution. Can be supplied as a list, where each element is the list of parameters to set in the distribution, or as an object coercable todata.frame, where each column is a parameter and each row is a distribution. See examples in VectorDistribution.shared_params(list())
If any parameters are shared when using thedistributionconstructor, this provides a much faster implementation to list and query them together. See examples in VectorDistribution.name(character(1))
Optional name of wrapped distribution.short_name(character(1))
Optional short name/ID of wrapped distribution.decorators(character())
Decorators to add to the distribution during construction.vecdistVectorDistribution
Alternative constructor to directly create this object from an object inheriting from VectorDistribution.ids(character())
Optional ids for wrapped distributions in vector, should be unique and of same length as the number of distributions.
Examples
MixtureDistribution$new(list(Binomial$new(prob = 0.5, size = 10), Binomial$new()), weights = c(0.2, 0.8) )
Method strprint()
Printable string representation of the MixtureDistribution. Primarily used internally.
Usage
MixtureDistribution$strprint(n = 10)
Arguments
n(integer(1))
Number of distributions to include when printing.
Method pdf()
Probability density function of the mixture distribution. Computed by
f_M(x) = ∑_i (f_i)(x)*w_i
where w_i is the vector of weights and f_i are the pdfs of the wrapped distributions.
Note that as this class inherits from VectorDistribution, it is possible to evaluate the distributions at different points, but that this is not the usual use-case for mixture distributions.
Usage
MixtureDistribution$pdf(..., log = FALSE, simplify = TRUE, data = NULL)
Arguments
...(numeric())
Points to evaluate the function at Arguments do not need to be named. The length of each argument corresponds to the number of points to evaluate, the number of arguments corresponds to the number of variables in the distribution. See examples.log(logical(1))
IfTRUEreturns the logarithm of the probabilities. Default isFALSE.simplifylogical(1)
IfTRUE(default) simplifies the return if possible to anumeric, otherwise returns a data.table::data.table.dataarray
Alternative method to specify points to evaluate. If univariate then rows correspond with number of points to evaluate and columns correspond with number of variables to evaluate. In the special case of VectorDistributions of multivariate distributions, then the third dimension corresponds to the distribution in the vector to evaluate.
Examples
m <- MixtureDistribution$new(list(Binomial$new(prob = 0.5, size = 10), Binomial$new()), weights = c(0.2, 0.8) ) m$pdf(1:5) m$pdf(1) # also possible but unlikely to be used m$pdf(1, 2)
Method cdf()
Cumulative distribution function of the mixture distribution. Computed by
F_M(x) = ∑_i (F_i)(x)*w_i
where w_i is the vector of weights and F_i are the cdfs of the wrapped distributions.
Usage
MixtureDistribution$cdf( ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE, data = NULL )
Arguments
...(numeric())
Points to evaluate the function at Arguments do not need to be named. The length of each argument corresponds to the number of points to evaluate, the number of arguments corresponds to the number of variables in the distribution. See examples. @examples m <- MixtureDistribution$new(list(Binomial$new(prob = 0.5, size = 10), Binomial$new()), weights = c(0.2, 0.8) ) m$cdf(1:5)lower.tail(logical(1))
IfTRUE(default), probabilities areX <= x, otherwise,P(X > x).log.p(logical(1))
IfTRUEreturns the logarithm of the probabilities. Default isFALSE.simplifylogical(1)
IfTRUE(default) simplifies the return if possible to anumeric, otherwise returns a data.table::data.table.dataarray
Alternative method to specify points to evaluate. If univariate then rows correspond with number of points to evaluate and columns correspond with number of variables to evaluate. In the special case of VectorDistributions of multivariate distributions, then the third dimension corresponds to the distribution in the vector to evaluate.
Method quantile()
The quantile function is not implemented for mixture distributions.
Usage
MixtureDistribution$quantile( ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE, data = NULL )
Arguments
...(numeric())
Points to evaluate the function at Arguments do not need to be named. The length of each argument corresponds to the number of points to evaluate, the number of arguments corresponds to the number of variables in the distribution. See examples.lower.tail(logical(1))
IfTRUE(default), probabilities areX <= x, otherwise,P(X > x).log.p(logical(1))
IfTRUEreturns the logarithm of the probabilities. Default isFALSE.simplifylogical(1)
IfTRUE(default) simplifies the return if possible to anumeric, otherwise returns a data.table::data.table.dataarray
Alternative method to specify points to evaluate. If univariate then rows correspond with number of points to evaluate and columns correspond with number of variables to evaluate. In the special case of VectorDistributions of multivariate distributions, then the third dimension corresponds to the distribution in the vector to evaluate.
Method rand()
Simulation function for mixture distributions. Samples are drawn from a mixture by first sampling Multinomial(probs = weights, size = n), then sampling each distribution according to the samples from the Multinomial, and finally randomly permuting these draws.
Usage
MixtureDistribution$rand(n, simplify = TRUE)
Arguments
n(numeric(1))
Number of points to simulate from the distribution. If length greater than 1, thenn <- length(n),simplifylogical(1)
IfTRUE(default) simplifies the return if possible to anumeric, otherwise returns a data.table::data.table.
Examples
m <- MixtureDistribution$new(distribution = "Normal", params = data.frame(mean = 1:2, sd = 1)) m$rand(5)
Method clone()
The objects of this class are cloneable with this method.
Usage
MixtureDistribution$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
See Also
Other wrappers:
Convolution,
DistributionWrapper,
HuberizedDistribution,
ProductDistribution,
TruncatedDistribution,
VectorDistribution
Examples
## ------------------------------------------------ ## Method `MixtureDistribution$new` ## ------------------------------------------------ MixtureDistribution$new(list(Binomial$new(prob = 0.5, size = 10), Binomial$new()), weights = c(0.2, 0.8) ) ## ------------------------------------------------ ## Method `MixtureDistribution$pdf` ## ------------------------------------------------ m <- MixtureDistribution$new(list(Binomial$new(prob = 0.5, size = 10), Binomial$new()), weights = c(0.2, 0.8) ) m$pdf(1:5) m$pdf(1) # also possible but unlikely to be used m$pdf(1, 2) ## ------------------------------------------------ ## Method `MixtureDistribution$rand` ## ------------------------------------------------ m <- MixtureDistribution$new(distribution = "Normal", params = data.frame(mean = 1:2, sd = 1)) m$rand(5)
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