A generalised distribution object for defining custom probability distributions as well as serving as the parent class to specific, familiar distributions.
Returns R6 object of class Distribution.
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
decoratorsReturns decorators currently used to decorate the distribution.
traitsReturns distribution traits.
valueSupportDeprecated, use $traits$valueSupport.
variateFormDeprecated, use $traits$variateForm.
typeDeprecated, use $traits$type.
propertiesReturns distribution properties, including skewness type and symmetry.
supportDeprecated, use $properties$type.
symmetryDeprecated, use $properties$symmetry.
supReturns supremum (upper bound) of the distribution support.
infReturns infimum (lower bound) of the distribution support.
dmaxReturns maximum of the distribution support.
dminReturns minimum of the distribution support.
kurtosisTypeDeprecated, use $properties$kurtosis.
skewnessTypeDeprecated, use $properties$skewness.
new()Creates a new instance of this R6 class.
Distribution$new( name = NULL, short_name = NULL, type, support = NULL, symmetric = FALSE, pdf = NULL, cdf = NULL, quantile = NULL, rand = NULL, parameters = NULL, decorators = NULL, valueSupport = NULL, variateForm = NULL, description = NULL, .suppressChecks = FALSE )
namecharacter(1)
Full name of distribution.
short_namecharacter(1)
Short name of distribution for printing.
type([set6::Set])
Distribution type.
support([set6::Set])
Distribution support.
symmetriclogical(1)
Symmetry type of the distribution.
pdffunction(1)
Probability density function of the distribution. At least one of pdf and
cdf must be provided.
cdffunction(1)
Cumulative distribution function of the distribution. At least one of pdf and
cdf must be provided.
quantilefunction(1)
Quantile (inverse-cdf) function of the distribution.
randfunction(1)
Simulation function for drawing random samples from the distribution.
parameters([param6::ParameterSet])
Parameter set for defining the parameters in the distribution, which should be set before
construction.
decorators(character())
Decorators to add to the distribution during construction.
valueSupport(character(1))
The support type of the distribution, one of "discrete", "continuous", "mixture".
If NULL, determined automatically.
variateForm(character(1))
The variate type of the distribution, one of "univariate", "multivariate", "matrixvariate".
If NULL, determined automatically.
description(character(1))
Optional short description of the distribution.
.suppressChecks(logical(1))
Used internally.
strprint()Printable string representation of the Distribution. Primarily used internally.
Distribution$strprint(n = 2)
n(integer(1))
Number of parameters to display when printing.
print()Prints the Distribution.
Distribution$print(n = 2, ...)
n(integer(1))
Passed to $strprint.
...ANY
Unused. Added for consistency.
summary()Prints a summary of the Distribution.
Distribution$summary(full = TRUE, ...)
full(logical(1))
If TRUE (default) prints a long summary of the distribution,
otherwise prints a shorter summary.
...ANY
Unused. Added for consistency.
parameters()Returns the full parameter details for the supplied parameter.
Distribution$parameters(id = NULL)
idDeprecated.
getParameterValue()Returns the value of the supplied parameter.
Distribution$getParameterValue(id, error = "warn")
idcharacter()
id of parameter value to return.
error(character(1))
If "warn" then returns a warning on error, otherwise breaks if "stop".
setParameterValue()Sets the value(s) of the given parameter(s).
Distribution$setParameterValue( ..., lst = list(...), error = "warn", resolveConflicts = FALSE )
...ANY
Named arguments of parameters to set values for. See examples.
lst(list(1))
Alternative argument for passing parameters. List names should be parameter names and list values
are the new values to set.
error(character(1))
If "warn" then returns a warning on error, otherwise breaks if "stop".
resolveConflicts(logical(1))
If FALSE (default) throws error if conflicting parameterisations are provided, otherwise
automatically resolves them by removing all conflicting parameters.
b = Binomial$new() b$setParameterValue(size = 4, prob = 0.4) b$setParameterValue(lst = list(size = 4, prob = 0.4))
pdf()For discrete distributions the probability mass function (pmf) is returned, defined as $$p_X(x) = P(X = x)$$ for continuous distributions the probability density function (pdf), \(f_X\), is returned $$f_X(x) = P(x < X \le x + dx)$$ for some infinitesimally small \(dx\).
If available a pdf will be returned using an analytic expression. Otherwise,
if the distribution has not been decorated with FunctionImputation, NULL is
returned.
Distribution$pdf(..., log = FALSE, simplify = TRUE, data = NULL)
...(numeric())
Points to evaluate the function at Arguments do not need
to be named. The length of each argument corresponds to the number of points to evaluate,
the number of arguments corresponds to the number of variables in the distribution.
See examples.
log(logical(1))
If TRUE returns the logarithm of the probabilities. Default is FALSE.
simplifylogical(1)
If TRUE (default) simplifies the return if possible to a numeric, otherwise returns a
data.table::data.table.
dataarray Alternative method to specify points to evaluate. If univariate then rows correspond with number of points to evaluate and columns correspond with number of variables to evaluate. In the special case of VectorDistributions of multivariate distributions, then the third dimension corresponds to the distribution in the vector to evaluate.
b <- Binomial$new() b$pdf(1:10) b$pdf(1:10, log = TRUE) b$pdf(data = matrix(1:10))
mvn <- MultivariateNormal$new() mvn$pdf(1, 2) mvn$pdf(1:2, 3:4) mvn$pdf(data = matrix(1:4, nrow = 2), simplify = FALSE)
cdf()The (lower tail) cumulative distribution function, \(F_X\), is defined as
$$F_X(x) = P(X \le x)$$
If lower.tail is FALSE then \(1 - F_X(x)\) is returned, also known as the
survival function.
If available a cdf will be returned using an analytic expression. Otherwise,
if the distribution has not been decorated with FunctionImputation, NULL is
returned.
Distribution$cdf( ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE, data = NULL )
...(numeric())
Points to evaluate the function at Arguments do not need
to be named. The length of each argument corresponds to the number of points to evaluate,
the number of arguments corresponds to the number of variables in the distribution.
See examples.
lower.tail(logical(1))
If TRUE (default), probabilities are X <= x, otherwise, P(X > x).
log.p(logical(1))
If TRUE returns the logarithm of the probabilities. Default is FALSE.
simplifylogical(1)
If TRUE (default) simplifies the return if possible to a numeric, otherwise returns a
data.table::data.table.
dataarray Alternative method to specify points to evaluate. If univariate then rows correspond with number of points to evaluate and columns correspond with number of variables to evaluate. In the special case of VectorDistributions of multivariate distributions, then the third dimension corresponds to the distribution in the vector to evaluate.
b <- Binomial$new() b$cdf(1:10) b$cdf(1:10, log.p = TRUE, lower.tail = FALSE) b$cdf(data = matrix(1:10))
quantile()The quantile function, \(q_X\), is the inverse cdf, i.e. $$q_X(p) = F^{-1}_X(p) = \inf\{x \in R: F_X(x) \ge p\}$$ #nolint
If lower.tail is FALSE then \(q_X(1-p)\) is returned.
If available a quantile will be returned using an analytic expression. Otherwise,
if the distribution has not been decorated with FunctionImputation, NULL is
returned.
Distribution$quantile( ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE, data = NULL )
...(numeric())
Points to evaluate the function at Arguments do not need
to be named. The length of each argument corresponds to the number of points to evaluate,
the number of arguments corresponds to the number of variables in the distribution.
See examples.
lower.tail(logical(1))
If TRUE (default), probabilities are X <= x, otherwise, P(X > x).
log.p(logical(1))
If TRUE returns the logarithm of the probabilities. Default is FALSE.
simplifylogical(1)
If TRUE (default) simplifies the return if possible to a numeric, otherwise returns a
data.table::data.table.
dataarray Alternative method to specify points to evaluate. If univariate then rows correspond with number of points to evaluate and columns correspond with number of variables to evaluate. In the special case of VectorDistributions of multivariate distributions, then the third dimension corresponds to the distribution in the vector to evaluate.
b <- Binomial$new() b$quantile(0.42) b$quantile(log(0.42), log.p = TRUE, lower.tail = TRUE) b$quantile(data = matrix(c(0.1,0.2)))
rand()The rand function draws n simulations from the distribution.
If available simulations will be returned using an analytic expression. Otherwise,
if the distribution has not been decorated with FunctionImputation, NULL is
returned.
Distribution$rand(n, simplify = TRUE)
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.
b <- Binomial$new() b$rand(10)
mvn <- MultivariateNormal$new() mvn$rand(5)
prec()Returns the precision of the distribution as 1/self$variance().
Distribution$prec()
stdev()Returns the standard deviation of the distribution as sqrt(self$variance()).
Distribution$stdev()
median()Returns the median of the distribution. If an analytical expression is available
returns distribution median, otherwise if symmetric returns self$mean, otherwise
returns self$quantile(0.5).
Distribution$median(na.rm = NULL, ...)
na.rm(logical(1))
Ignored, addded for consistency.
...ANY
Ignored, addded for consistency.
iqr()Inter-quartile range of the distribution. Estimated as
self$quantile(0.75) - self$quantile(0.25).
Distribution$iqr()
confidence()1 or 2-sided confidence interval around distribution.
Distribution$confidence(alpha = 0.95, sides = "both", median = FALSE)
alpha(numeric(1)) Level of confidence, default is 95%
sides(character(1)) One of 'lower', 'upper' or 'both'
median(logical(1)) If TRUE also returns median
correlation()If univariate returns 1, otherwise returns the distribution correlation.
Distribution$correlation()
liesInSupport()Tests if the given values lie in the support of the distribution.
Uses [set6::Set]$contains.
Distribution$liesInSupport(x, all = TRUE, bound = FALSE)
xANY
Values to test.
alllogical(1)
If TRUE (default) returns TRUE if all x are in the distribution,
otherwise returns a vector of logicals corresponding to each element in
x.
boundlogical(1)
If TRUE then tests if x lie between the upper and lower bounds of the distribution,
otherwise tests if x lie between the maximum and minimum of the distribution.
liesInType()Tests if the given values lie in the type of the distribution.
Uses [set6::Set]$contains.
Distribution$liesInType(x, all = TRUE, bound = FALSE)
xANY
Values to test.
alllogical(1)
If TRUE (default) returns TRUE if all x are in the distribution,
otherwise returns a vector of logicals corresponding to each element in
x.
boundlogical(1)
If TRUE then tests if x lie between the upper and lower bounds of the distribution,
otherwise tests if x lie between the maximum and minimum of the distribution.
workingSupport()Returns an estimate for the computational support of the distribution.
If an analytical cdf is available, then this is computed as the smallest interval
in which the cdf lower bound is 0 and the upper bound is 1, bounds are incremented in
10^i intervals. If no analytical cdf is available, then this is computed as the smallest
interval in which the lower and upper bounds of the pdf are 0, this is much less precise
and is more prone to error. Used primarily by decorators.
Distribution$workingSupport()
clone()The objects of this class are cloneable with this method.
Distribution$clone(deep = FALSE)
deepWhether to make a deep clone.
# NOT RUN {
## ------------------------------------------------
## Method `Distribution$setParameterValue`
## ------------------------------------------------
b = Binomial$new()
b$setParameterValue(size = 4, prob = 0.4)
b$setParameterValue(lst = list(size = 4, prob = 0.4))
## ------------------------------------------------
## Method `Distribution$pdf`
## ------------------------------------------------
b <- Binomial$new()
b$pdf(1:10)
b$pdf(1:10, log = TRUE)
b$pdf(data = matrix(1:10))
mvn <- MultivariateNormal$new()
mvn$pdf(1, 2)
mvn$pdf(1:2, 3:4)
mvn$pdf(data = matrix(1:4, nrow = 2), simplify = FALSE)
## ------------------------------------------------
## Method `Distribution$cdf`
## ------------------------------------------------
b <- Binomial$new()
b$cdf(1:10)
b$cdf(1:10, log.p = TRUE, lower.tail = FALSE)
b$cdf(data = matrix(1:10))
## ------------------------------------------------
## Method `Distribution$quantile`
## ------------------------------------------------
b <- Binomial$new()
b$quantile(0.42)
b$quantile(log(0.42), log.p = TRUE, lower.tail = TRUE)
b$quantile(data = matrix(c(0.1,0.2)))
## ------------------------------------------------
## Method `Distribution$rand`
## ------------------------------------------------
b <- Binomial$new()
b$rand(10)
mvn <- MultivariateNormal$new()
mvn$rand(5)
# }
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