Product Distribution Wrapper

A wrapper for creating the product distribution of multiple independent probability distributions.

# S3 method for Distribution
*(x, y)

Arguments

x, y

Distribution

Details

A product distribution is defined by

$$F_P(X1 = x1,...,XN = xN) = F_{X1}(x1) * ... * F_{XN}(xn)$$ #nolint where \(F_P\) is the cdf of the product distribution and \(X1,...,XN\) are independent distributions.

See also

Other wrappers: Convolution, DistributionWrapper, HuberizedDistribution, MixtureDistribution, TruncatedDistribution, VectorDistribution

Super classes

distr6::Distribution -> distr6::DistributionWrapper -> distr6::VectorDistribution -> ProductDistribution

Methods

Public methods

• ProductDistribution$new()

• ProductDistribution$strprint()

• ProductDistribution$pdf()

• ProductDistribution$cdf()

• ProductDistribution$quantile()

• ProductDistribution$clone()

Inherited methods

• distr6::Distribution$confidence()
• distr6::Distribution$correlation()
• distr6::Distribution$iqr()
• distr6::Distribution$liesInSupport()
• distr6::Distribution$liesInType()
• distr6::Distribution$parameters()
• distr6::Distribution$prec()
• distr6::Distribution$print()
• distr6::Distribution$setParameterValue()
• distr6::Distribution$stdev()
• distr6::Distribution$summary()
• distr6::Distribution$workingSupport()
• distr6::VectorDistribution$cf()
• distr6::VectorDistribution$entropy()
• distr6::VectorDistribution$getParameterValue()
• distr6::VectorDistribution$kurtosis()
• distr6::VectorDistribution$mean()
• distr6::VectorDistribution$median()
• distr6::VectorDistribution$mgf()
• distr6::VectorDistribution$mode()
• distr6::VectorDistribution$pgf()
• distr6::VectorDistribution$rand()
• distr6::VectorDistribution$skewness()
• distr6::VectorDistribution$variance()
• distr6::VectorDistribution$wrappedModels()

---

Method new()

Creates a new instance of this R6 class.

Usage

ProductDistribution$new(
  distlist = NULL,
  distribution = NULL,
  params = NULL,
  shared_params = NULL,
  name = NULL,
  short_name = NULL,
  decorators = NULL,
  vecdist = NULL,
  ids = NULL
)

Arguments

distlist

(list())
List of Distributions.

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.

vecdist

VectorDistribution
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

\dontrun{
ProductDistribution$new(list(Binomial$new(
  prob = 0.5,
  size = 10
), Normal$new(mean = 15)))

ProductDistribution$new(
  distribution = "Binomial",
  params = list(
    list(prob = 0.1, size = 2),
    list(prob = 0.6, size = 4),
    list(prob = 0.2, size = 6)
  )
)

# Equivalently
ProductDistribution$new(
  distribution = "Binomial",
  params = data.table::data.table(prob = c(0.1, 0.6, 0.2), size = c(2, 4, 6))
)
}

---

Method strprint()

Printable string representation of the ProductDistribution. Primarily used internally.

Usage

ProductDistribution$strprint(n = 10)

Arguments

n

(integer(1))
Number of distributions to include when printing.

---

Method pdf()

Probability density function of the product distribution. Computed by $$f_P(X1 = x1,...,XN = xN) = \prod_{i} f_{Xi}(xi)$$ where \(f_{Xi}\) are the pdfs of the wrapped distributions.

Usage

ProductDistribution$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.

simplify

logical(1)
If TRUE (default) simplifies the return if possible to a numeric, otherwise returns a data.table::data.table.

data

array
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

p <- ProductDistribution$new(list(
Binomial$new(prob = 0.5, size = 10),
Binomial$new()))
p$pdf(1:5)
p$pdf(1, 2)
p$pdf(1:2)

---

Method cdf()

Cumulative distribution function of the product distribution. Computed by $$F_P(X1 = x1,...,XN = xN) = \prod_{i} F_{Xi}(xi)$$ where \(F_{Xi}\) are the cdfs of the wrapped distributions.

Usage

ProductDistribution$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.

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.

simplify

logical(1)
If TRUE (default) simplifies the return if possible to a numeric, otherwise returns a data.table::data.table.

data

array
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

p <- ProductDistribution$new(list(
Binomial$new(prob = 0.5, size = 10),
Binomial$new()))
p$cdf(1:5)
p$cdf(1, 2)
p$cdf(1:2)

---

Method quantile()

The quantile function is not implemented for product distributions.

Usage

ProductDistribution$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.

simplify

logical(1)
If TRUE (default) simplifies the return if possible to a numeric, otherwise returns a data.table::data.table.

data

array
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 clone()

The objects of this class are cloneable with this method.

Usage

ProductDistribution$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

## ------------------------------------------------
## Method `ProductDistribution$new`
## ------------------------------------------------

if (FALSE) {
ProductDistribution$new(list(Binomial$new(
  prob = 0.5,
  size = 10
), Normal$new(mean = 15)))

ProductDistribution$new(
  distribution = "Binomial",
  params = list(
    list(prob = 0.1, size = 2),
    list(prob = 0.6, size = 4),
    list(prob = 0.2, size = 6)
  )
)

# Equivalently
ProductDistribution$new(
  distribution = "Binomial",
  params = data.table::data.table(prob = c(0.1, 0.6, 0.2), size = c(2, 4, 6))
)
}

## ------------------------------------------------
## Method `ProductDistribution$pdf`
## ------------------------------------------------

p <- ProductDistribution$new(list(
Binomial$new(prob = 0.5, size = 10),
Binomial$new()))
p$pdf(1:5)
#> [1] 9.536743e-05 1.931190e-03 1.373291e-02 4.205704e-02 6.056213e-02
p$pdf(1, 2)
#> [1] 0.0004291534
p$pdf(1:2)
#> [1] 9.536743e-05 1.931190e-03

## ------------------------------------------------
## Method `ProductDistribution$cdf`
## ------------------------------------------------

p <- ProductDistribution$new(list(
Binomial$new(prob = 0.5, size = 10),
Binomial$new()))
p$cdf(1:5)
#> [1] 0.0001153946 0.0029907227 0.0295410156 0.1420936584 0.3881874084
p$cdf(1, 2)
#> [1] 0.0005874634
p$cdf(1:2)
#> [1] 0.0001153946 0.0029907227
Normal$new() * Binomial$new()
#> Norm X Binom