| Title: | Algebra over Probability Distributions |
| Version: | 0.1.0 |
| Description: | Provides an algebra over probability distributions enabling composition, sampling, and automatic simplification to closed forms. Supports normal, exponential, multivariate normal, and empirical distributions with operations like addition and subtraction that automatically simplify when mathematical identities apply (e.g., the sum of independent normal distributions is normal). Uses S3 classes for distributions and R6 for support objects. |
| License: | GPL (≥ 3) |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| Suggests: | knitr, rmarkdown, testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| Imports: | stats, mvtnorm, R6 |
| Depends: | R (≥ 3.5.0) |
| VignetteBuilder: | knitr |
| URL: | https://github.com/queelius/algebraic.dist, https://queelius.github.io/algebraic.dist/ |
| BugReports: | https://github.com/queelius/algebraic.dist/issues |
| NeedsCompilation: | no |
| Packaged: | 2025-12-11 17:29:33 UTC; spinoza |
| Author: | Alexander Towell 
[aut, cre] |
| Maintainer: | Alexander Towell <lex@metafunctor.com> |
| Repository: | CRAN |
| Date/Publication: | 2025-12-17 10:50:02 UTC |
Method for adding dist objects.
Description
Creates an expression distribution and automatically simplifies to closed form when possible (e.g., normal + normal = normal).
Usage
## S3 method for class 'dist'
x + y
Arguments
x |
The first |
y |
The second |
Value
A simplified distribution or edist if no closed form exists
Method for negation or subtraction of dist objects.
Description
Unary: returns negated distribution (e.g., -N(mu, var) = N(-mu, var)) Binary: creates expression distribution and simplifies to closed form when possible (e.g., normal - normal = normal).
Usage
## S3 method for class 'dist'
x - y
Arguments
x |
The first |
y |
The second |
Value
A simplified distribution or edist if no closed form exists
Generic method for obtaining the cdf of an object.
Description
Generic method for obtaining the cdf of an object.
Usage
cdf(x, ...)
Arguments
x |
The object to obtain the cdf of. |
... |
Additional arguments to pass. |
Method for obtaining the cdf of empirical_dist object x.
Description
If x is a multivariate empirical distribution, this function will
throw an error. It's only defined for univariate empirical distributions.
Usage
## S3 method for class 'empirical_dist'
cdf(x, ...)
Arguments
x |
The empirical distribution object. |
... |
Additional arguments to pass (not used)) |
Value
A function that takes a numeric vector t and returns the
empirical cdf of x evaluated at t.
Method to obtain the cdf of an exponential object.
Description
Method to obtain the cdf of an exponential object.
Usage
## S3 method for class 'exponential'
cdf(x, ...)
Arguments
x |
The object to obtain the pdf of |
... |
Additional arguments (not used) |
Value
A function that computes the cdf of the exponential. Accepts as
input a vector t at which to compute the cdf, an input rate
denoting the failure rate of the exponential distribution, and a
logical log indicating whether to compute the log of the cdf.
By default, rate is the failure rate of object x.
Method for obtaining the CDF of a mvn object.
Description
Method for obtaining the CDF of a mvn object.
Usage
## S3 method for class 'mvn'
cdf(x, ...)
Arguments
x |
The object to obtain the CDF of |
... |
Additional arguments to pass (not used) |
Method for obtaining the cdf of an normal object.
Description
Method for obtaining the cdf of an normal object.
Usage
## S3 method for class 'normal'
cdf(x, ...)
Arguments
x |
The object to obtain the cdf of |
... |
Additional arguments to pass (not used) |
Value
A function that computes the cdf of the normal distribution.
It accepts as input a parameter vector q, a mean vector mu,
a variance var, and a log argument
determining whether to compute the log of the cdf. By default,
mu and var are the mean and variance of object x and log
is FALSE. Finally, it accepts additional arguments ... to
pass to the pnorm function.
Generic method for obtaining the conditional distribution of a distribution
object x given condition P.
Description
Generic method for obtaining the conditional distribution of a distribution
object x given condition P.
Usage
conditional(x, P, ...)
Arguments
x |
The empirical distribution object. |
P |
The predicate function to condition |
... |
additional arguments to pass into |
Method for obtaining the condition distribution, x | P(x), of
dist object x.
Description
We just sample from x and place the sample in empirical_dist and
then condition on it.
Usage
## S3 method for class 'dist'
conditional(x, P, n = 10000L, ...)
Arguments
x |
The distribution object. |
P |
The predicate function to condition the distribution on |
n |
The number of samples to generate for the MC estimate of the conditional distribution x | P. Defaults to 10000. |
... |
additional arguments to pass into |
Method for obtaining the condition distribution, x | P(x), of
empirical_dist object x.
Description
In other words, we condition the data on the predicate function. In order to do so, we simply remove all rows from the data that do not satisfy the predicate P. For instance, if we have a 2-dimensional distribution, and we want to condition on the first dimension being greater than the second dimension, we would do the following:
Usage
## S3 method for class 'empirical_dist'
conditional(x, P, ...)
Arguments
x |
The empirical distribution object. |
P |
The predicate function to condition the data on. |
... |
additional arguments to pass into |
Details
x_cond <- conditional(x, function(d) d[1] > d[2])
This would return a new empirical distribution object with the same
dimensionality as x, but with all rows where the first dimension is
less than or equal to the second dimension removed.
Method for obtaining the pdf of a empirical_dist object.
Description
Method for obtaining the pdf of a empirical_dist object.
Usage
## S3 method for class 'empirical_dist'
density(x, ...)
Arguments
x |
The object to obtain the pdf of. |
... |
Additional arguments to pass into the pdf function. |
Note
sort tibble lexicographically and do a binary search to find upper
and lower bound in log(nobs(x)) time.
Method to obtain the pdf of an exponential object.
Description
Method to obtain the pdf of an exponential object.
Usage
## S3 method for class 'exponential'
density(x, ...)
Arguments
x |
The object to obtain the pdf of |
... |
Additional arguments (not used) |
Value
A function that computes the pdf of the exponential distribution
at a given point t. Also accepts a rate argument that
determines the failure rate of the exponential distribution (defaults
to the failure rate of object x) and a log argument that determines
whether to compute the log of the pdf.
Function generator for obtaining the pdf of an mvn object (multivariate
normal).
Description
Function generator for obtaining the pdf of an mvn object (multivariate
normal).
Usage
## S3 method for class 'mvn'
density(x, ...)
Arguments
x |
The |
... |
Additional arguments to pass into the generated function. |
Value
A function that computes the pdf of the mvn distribution.
It accepts as input:
- obs: vector or matrix of quantiles. when x is a matrix, each row
is taken to be a quantile and columns correspond to the number of
dimensions, p.
- mu: a a vector denoting the population mean. Defaults to the
mean of x (an mvn object)
- sigma: a matrix denoting the variance-covariance of
observations. Defaults to the variance-covariance of x.
- log: logical, determines whether to compute the log of the pdf.
Defaults to FALSE.
- ...: any additional parameters to pass to dmvnorm.
Method for obtaining the pdf of an normal object.
Description
Method for obtaining the pdf of an normal object.
Usage
## S3 method for class 'normal'
density(x, ...)
Arguments
x |
The object to obtain the pdf of |
... |
Additional arguments to pass (not used) |
Value
A function that computes the pdf of the normal distribution.
It accepts as input a parameter vector x, a mean vector mu,
a variance-covariance matrix var, and a log argument
determining whether to compute the log of the pdf. By default,
mu and var are the mean and variance of object x.
Method for obtaining the dimension of a empirical_dist object.
Description
Method for obtaining the dimension of a empirical_dist object.
Usage
## S3 method for class 'empirical_dist'
dim(x)
Arguments
x |
The object to obtain the dimension of. |
Method to obtain the dimension of an exponential object.
Description
Method to obtain the dimension of an exponential object.
Usage
## S3 method for class 'exponential'
dim(x)
Arguments
x |
The |
Value
The dimension of the exponential object
Return the dimension of the finite set.
Description
Return the dimension of the finite set.
Usage
## S3 method for class 'finite_set'
dim(x)
Arguments
x |
A finite set. |
Return the dimension of the interval.
Description
Return the dimension of the interval.
Usage
## S3 method for class 'interval'
dim(x)
Arguments
x |
An interval object. |
Method for obtaining the dimension of an mvn object.
Description
Method for obtaining the dimension of an mvn object.
Usage
## S3 method for class 'mvn'
dim(x)
Arguments
x |
The object to obtain the dimension of |
Value
The dimension of the mvn object
Method for obtaining the dimension of a normal object.
Description
Method for obtaining the dimension of a normal object.
Usage
## S3 method for class 'normal'
dim(x)
Arguments
x |
The |
Value
The dimension of the normal object
Takes an expression e and a list vars and returns a
lazy edist (expression distribution object), that is a subclass
of dist that can be used in place of a dist object.
Description
Takes an expression e and a list vars and returns a
lazy edist (expression distribution object), that is a subclass
of dist that can be used in place of a dist object.
Usage
edist(e, vars)
Arguments
e |
the expression to evaluate against the arguments. |
vars |
the list of distributions (with variable names)
to evaluate the expression |
Value
An edist object.
Construct empirical distribution object.
Description
Construct empirical distribution object.
Usage
empirical_dist(data)
Arguments
data |
data to construct empirical distribution from. if matrix or data frame, each row is a joint observation, if a vector, each element is an observation. whatever data is, it must be convertible to a tibble. |
Generic method for obtaining the expectation of f with respect to
x.
Description
Generic method for obtaining the expectation of f with respect to
x.
Usage
expectation(x, g, ...)
Arguments
x |
The distribution object. |
g |
The function to take the expectation of. |
... |
Additional arguments to pass into |
Expectation of a Function Applied to a dist Object
Description
Expectation operator applied to x of type dist
with respect to a function g. Optionally, constructs a confidence interval
for the expectation estimate using the Central Limit Theorem.
Usage
## S3 method for class 'dist'
expectation(x, g = function(t) t, ..., control = list())
Arguments
x |
A |
g |
Characteristic function of interest, defaults to identity. |
... |
Additional arguments to pass to |
control |
A list of control parameters: compute_stats - Logical, whether to compute CIs for the expectations, defaults to FALSE n - Integer, the number of samples to use for the MC estimate, defaults to 10000L alpha - Real, the significance level for the confidence interval, defaults to 0.05 |
Value
If compute_stats is FALSE, then the estimate of the expectation,
otherwise a list with the following components:
value - The estimate of the expectation
ci - The confidence intervals for each component of the expectation
n - The number of samples
Method for obtaining the expectation of empirical_dist object x
under function g.
Description
Method for obtaining the expectation of empirical_dist object x
under function g.
Usage
## S3 method for class 'empirical_dist'
expectation(x, g = function(t) t, ..., control = list())
Arguments
x |
The distribution object. |
g |
The function to take the expectation of. |
... |
Additional arguments to pass into function |
control |
a list of control parameters: compute_stats - Whether to compute CIs for the expectations, defaults to FALSE n - The number of samples to use for the MC estimate, defaults to 10000 alpha - The significance level for the confidence interval, defaults to 0.05 |
Value
If compute_stats is FALSE, then the estimate of the expectation,
otherwise a list with the following components:
value - The estimate of the expectation
ci - The confidence intervals for each component of the expectation
n - The number of samples
Method for obtaining the expectation of f with respect to a
univariate_dist object x.
Description
Assumes the support is a contiguous interval that has operations for retrieving the lower and upper bounds.
Usage
## S3 method for class 'univariate_dist'
expectation(x, g, ..., control = list())
Arguments
x |
The distribution object. |
g |
The function to take the expectation of. |
... |
Additional arguments to pass into |
control |
An (optional) list of control parameters for |
Function used for computing expectations given data (e.g., from an MC
simulation or bootstrap). it expects a matrix, or something that can be
coerced to a matrix (e.g., a data frame). it also expects a function g to
apply to each row of the data, and returns the expectation of g under the
empirical distribution of the data. it also returns a confidence interval for
the expectation, and the number of samples used to compute the expectation.
Description
example: expectation_data(D, function(x) (x-colMeans(D)) %*% t(x-colMeans(D))) computes the covariance of the data D, except the matrix structure is lost (it's just a vector, which can be coerced back to a matrix if needed).
Usage
expectation_data(
data,
g = function(x) x,
...,
compute_stats = TRUE,
alpha = 0.05
)
Arguments
data |
a matrix of data |
g |
a function to apply to each row of the data |
... |
additional arguments to pass to |
compute_stats |
whether to compute CIs for the expectations |
alpha |
the confidence level for the confidence interval for each component of the expectation (if compute_stats is TRUE) |
Value
if compute_stats is TRUE, then a list with the following components: value - The estimate of the expectation ci - The confidence intervals for each component of the expectation n - The number of samples otherwise, just the value of the expectation.
Construct exponential distribution object.
Description
Construct exponential distribution object.
Usage
exponential(rate)
Arguments
rate |
failure rate |
Finite set
Description
A finite set. It also satisfies the concept of a support.
Public fields
valuesA vector of values.
Methods
Public methods
Method new()
Initialize a finite set.
Usage
finite_set$new(values)
Arguments
valuesA vector of values.
Method has()
Determine if a value is contained in the finite set.
Usage
finite_set$has(x)
Arguments
xA vector of values.
Method infimum()
Get the infimum of the finite set.
Usage
finite_set$infimum()
Returns
A numeric vector of infimums.
Method supremum()
Get the supremum of the finite set.
Usage
finite_set$supremum()
Returns
A numeric vector of supremums.
Method dim()
Get the dimension of the finite set.
Usage
finite_set$dim()
Returns
The dimension of the finite set.
Method clone()
The objects of this class are cloneable with this method.
Usage
finite_set$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Support
Description
support is a class that represents the support of a random element or distribution, i.e. the set of values that it realize.
It's a conceptual class. To satisfy the concept of a support, the following methods must be implemented:
has: a function that returns a logical vector indicating whether each value in a vector is contained in the support
infimum: a function that returns the infimum of the support
supremum: a function that returns the supremum of the support
dim: a function that returns the dimension of the support
We provide two implementations that satisfy the concept:
-
interval: a support that is an infiite set of contiguous numeric values -
finite_set: a support that is a finite set of values Determine if a value is contained in the support.
Usage
has(object, x)
Arguments
object |
A support object. |
x |
A vector of values. |
Determine if a value is contained in the finite set.
Description
Determine if a value is contained in the finite set.
Usage
## S3 method for class 'finite_set'
has(object, x)
Arguments
object |
A finite set. |
x |
A vector of values. |
Determine if a value is contained in the interval.
Description
Determine if a value is contained in the interval.
Usage
## S3 method for class 'interval'
has(object, x)
Arguments
object |
An interval object. |
x |
A vector of values. |
Generic method for obtaining the hazard function of an object.
Description
Generic method for obtaining the hazard function of an object.
Usage
hazard(x, ...)
Arguments
x |
The object to obtain the hazard function of. |
... |
Additional arguments to pass. |
Method to obtain the hazard function of an exponential object.
Description
Method to obtain the hazard function of an exponential object.
Usage
## S3 method for class 'exponential'
hazard(x, ...)
Arguments
x |
The |
... |
Additional arguments (not used) |
Value
A function that computes the hazard function of the
exponential distribution at a given point t and rate rate.
By default, rate is the failure rate of object x
Also accepts a log argument that determines whether
to compute the log of the hazard function.
Get the infimum of the support.
Description
Get the infimum of the support.
Usage
infimum(object)
Arguments
object |
A support object. |
Return the infimum of the finite set.
Description
Return the infimum of the finite set.
Usage
## S3 method for class 'finite_set'
infimum(object)
Arguments
object |
A finite set. |
Return the (vector of) infimum of the interval.
Description
Return the (vector of) infimum of the interval.
Usage
## S3 method for class 'interval'
infimum(object)
Arguments
object |
An interval object. |
Interval
Description
An interval is a support that is a finite union of intervals.
Public fields
lowerA numeric vector of lower bounds.
upperA numeric vector of upper bounds.
lower_closedA logical vector indicating whether the lower bound is closed.
upper_closedA logical vector indicating whether the upper bound is closed.
Methods
Public methods
Method new()
Initialize an interval.
Usage
interval$new( lower = -Inf, upper = Inf, lower_closed = FALSE, upper_closed = FALSE )
Arguments
lowerA numeric vector of lower bounds.
upperA numeric vector of upper bounds.
lower_closedA logical vector indicating whether the lower bound is closed.
upper_closedA logical vector indicating whether the upper bound is closed.
Method is_empty()
Determine if the interval is empty
Usage
interval$is_empty()
Returns
A logical vector indicating whether the interval is empty.
Method has()
Determine if a value is contained in the interval.
Usage
interval$has(x)
Arguments
xA numeric vector of values.
Returns
A logical vector indicating whether each value is contained
Method infimum()
Get the infimum of the interval.
Usage
interval$infimum()
Returns
A numeric vector of infimums.
Method supremum()
Get the supremum of the interval.
Usage
interval$supremum()
Returns
A numeric vector of supremums.
Method dim()
Get the dimension of the interval.
Usage
interval$dim()
Returns
The dimension of the interval.
Method clone()
The objects of this class are cloneable with this method.
Usage
interval$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Generic method for obtaining the quantile (inverse cdf) of an object.
Description
Generic method for obtaining the quantile (inverse cdf) of an object.
Usage
inv_cdf(x, ...)
Arguments
x |
The object to obtain the quantile of. |
... |
Additional arguments to pass. |
Method to obtain the inverse cdf of an exponential object.
Description
Method to obtain the inverse cdf of an exponential object.
Usage
## S3 method for class 'exponential'
inv_cdf(x, ...)
Arguments
x |
The object to obtain the inverse cdf of |
... |
Additional arguments (not used) |
Value
A function that computes the inverse cdf of the exponential
distribution. Accepts as input a vector p probabilities
to compute the inverse cdf, a rate value denoting the
failure rate of the exponential distribution, and a logical
log.p indicating whether input p denotes probability
or log-probability. By default, rate is the failure rate
of object x.
Method for obtaining the inverse cdf of an normal object.
Description
Method for obtaining the inverse cdf of an normal object.
Usage
## S3 method for class 'normal'
inv_cdf(x, ...)
Arguments
x |
The object to obtain the inverse cdf of |
... |
Additional arguments to pass (not used) |
Value
A function that computes the inverse cdf of the normal distribution.
Function to determine whether an object x is a dist object.
Description
Function to determine whether an object x is a dist object.
Usage
is_dist(x)
Arguments
x |
The object to test |
Value
Logical indicating whether x is a dist object.
Function to determine whether an object x is an edist object.
Description
Function to determine whether an object x is an edist object.
Usage
is_edist(x)
Arguments
x |
The object to test |
Function to determine whether an object x is an empirical_dist object.
Description
Function to determine whether an object x is an empirical_dist object.
Usage
is_empirical_dist(x)
Arguments
x |
The object to test |
Function to determine whether an object x is an exponential object.
Description
Function to determine whether an object x is an exponential object.
Usage
is_exponential(x)
Arguments
x |
The object to test |
Function to determine whether an object x is an mvn object.
Description
Function to determine whether an object x is an mvn object.
Usage
is_mvn(x)
Arguments
x |
The object to test |
Function to determine whether an object x is an normal object.
Description
Function to determine whether an object x is an normal object.
Usage
is_normal(x)
Arguments
x |
The object to test |
We have an edist object, which is a subclass of dist, and now we're placing it inside of a limit expression, where the limit is understood to be with respect to sample size. We need to define a method for this.
Description
We have an edist object, which is a subclass of dist, and now we're placing it inside of a limit expression, where the limit is understood to be with respect to sample size. We need to define a method for this.
Usage
limit.edist(x)
Arguments
x |
The edist object to take the limit of |
Value
The limit of the edist object
Generic method for obtaining the marginal distribution of a distribution
object x over components indices.
Description
Generic method for obtaining the marginal distribution of a distribution
object x over components indices.
Usage
marginal(x, indices)
Arguments
x |
The distribution object. |
indices |
The indices of the marginal distribution to obtain. |
Method for obtaining the marginal distribution of empirical_dist object
x.
Description
Method for obtaining the marginal distribution of empirical_dist object
x.
Usage
## S3 method for class 'empirical_dist'
marginal(x, indices)
Arguments
x |
The empirical distribution object. |
indices |
The indices of the marginal distribution to obtain. |
Generic method for obtaining the marginal distribution of an mvn object
x over components indices.
Description
Generic method for obtaining the marginal distribution of an mvn object
x over components indices.
Usage
## S3 method for class 'mvn'
marginal(x, indices)
Arguments
x |
The |
indices |
The indices of the marginal distribution to obtain. |
Method for obtaining the mean of an edist object.
Description
Method for obtaining the mean of an edist object.
Usage
## S3 method for class 'edist'
mean(x, n = 10000, ...)
Arguments
x |
The |
n |
The number of samples to take (default: 1000) |
... |
Additional arguments to pass (not used) |
Value
The mean of the edist object
Method for obtaining the mean of empirical_dist object x.
Description
Method for obtaining the mean of empirical_dist object x.
Usage
## S3 method for class 'empirical_dist'
mean(x, ...)
Arguments
x |
The distribution object. |
... |
Additional arguments to pass (not used). |
Method to obtain the mean of an exponential object.
Description
Method to obtain the mean of an exponential object.
Usage
## S3 method for class 'exponential'
mean(x, ...)
Arguments
x |
The |
... |
Additional arguments (not used) |
Retrieve the mean of a mvn object.
Description
Retrieve the mean of a mvn object.
Usage
## S3 method for class 'mvn'
mean(x, ...)
Arguments
x |
The |
... |
Additional arguments to pass (not used) |
Value
The mean of the mvn object
Retrieve the mean of a normal object.
Description
Retrieve the mean of a normal object.
Usage
## S3 method for class 'normal'
mean(x, ...)
Arguments
x |
The |
... |
Additional arguments to pass (not used) |
Value
The mean of the normal object
Method for obtaining the mean of univariate_dist object x.
Description
Method for obtaining the mean of univariate_dist object x.
Usage
## S3 method for class 'univariate_dist'
mean(x, ...)
Arguments
x |
The distribution object. |
... |
Additional arguments to pass into |
Construct a multivariate or univariate normal distribution object.
Description
This function constructs an object representing a normal distribution.
If the length of the mean vector mu is 1, it creates a univariate
normal distribution. Otherwise, it creates a multivariate normal distribution.
Usage
mvn(mu, sigma = diag(length(mu)))
Arguments
mu |
A numeric vector specifying the means of the distribution.
If |
sigma |
A numeric matrix specifying the variance-covariance matrix of the
distribution. It must be a square matrix with the same number of
rows and columns as the length of |
Value
If mu has length 1, it returns a normal object. If mu has length
> 1, it returns an mvn object. Both types of objects contain mu
and sigma as their properties.
Method for obtaining the number of observations used to construct a
empirical_dist object.
Description
Method for obtaining the number of observations used to construct a
empirical_dist object.
Usage
## S3 method for class 'empirical_dist'
nobs(object, ...)
Arguments
object |
The empirical distribution object. |
... |
Additional arguments to pass (not used). |
Construct univariate normal distribution object.
Description
Construct univariate normal distribution object.
Usage
normal(mu = 0, var = 1)
Arguments
mu |
mean |
var |
variance |
Generic method for obtaining the number of parameters of
distribution-like object x.
Description
Generic method for obtaining the number of parameters of
distribution-like object x.
Usage
nparams(x)
Arguments
x |
the object to obtain the number of parameters for |
Method for obtaining the name of a empirical_dist object. Since the
empirical distribution is parameter-free, this function returns 0.
Description
Method for obtaining the name of a empirical_dist object. Since the
empirical distribution is parameter-free, this function returns 0.
Usage
## S3 method for class 'empirical_dist'
nparams(x)
Arguments
x |
The empirical distribution object. |
Retrieve the observations used to construct a distribution-like object. This is useful for obtaining the data used to construct an empirical distribution, but it is also useful for, say, retrieving the sample that was used by a fitted object, like an maximum likelihood estimate.
Description
Retrieve the observations used to construct a distribution-like object. This is useful for obtaining the data used to construct an empirical distribution, but it is also useful for, say, retrieving the sample that was used by a fitted object, like an maximum likelihood estimate.
Usage
obs(x)
Arguments
x |
the object to retrieve the observations from |
Method for obtaining the observations used to construct a
empirical_dist object.
Description
Method for obtaining the observations used to construct a
empirical_dist object.
Usage
## S3 method for class 'empirical_dist'
obs(x)
Arguments
x |
The empirical distribution object. |
Generic method for obtaining the parameters of an object.
Description
Generic method for obtaining the parameters of an object.
Usage
params(x)
Arguments
x |
The object to obtain the parameters of. |
Method for obtaining the parameters of an edist object.
Description
Method for obtaining the parameters of an edist object.
Usage
## S3 method for class 'edist'
params(x)
Arguments
x |
The object to obtain the parameters of |
Value
A named vector of parameters
empirical_dist objects have no parameters, so this function returns NULL.
Description
empirical_dist objects have no parameters, so this function returns NULL.
Usage
## S3 method for class 'empirical_dist'
params(x)
Arguments
x |
The empirical distribution object. |
Method for obtaining the parameters of an exponential object.
Description
Method for obtaining the parameters of an exponential object.
Usage
## S3 method for class 'exponential'
params(x)
Arguments
x |
The object to obtain the parameters of |
Value
A named vector of parameters
Method for obtaining the parameters of a mvn object.
Description
Method for obtaining the parameters of a mvn object.
Usage
## S3 method for class 'mvn'
params(x)
Arguments
x |
The object to obtain the parameters of |
Value
A named vector of parameters
Method for obtaining the parameters of a normal object.
Description
Method for obtaining the parameters of a normal object.
Usage
## S3 method for class 'normal'
params(x)
Arguments
x |
The object to obtain the parameters of |
Value
A named vector of parameters
Method for printing an edist object.
Description
Method for printing an edist object.
Usage
## S3 method for class 'edist'
print(x, ...)
Arguments
x |
The object to print |
... |
Additional arguments to pass (not used) |
Method for printing a dist object
Description
Method for printing a dist object
Usage
## S3 method for class 'empirical_dist'
print(x, ...)
Arguments
x |
The object to print |
... |
Additional arguments to pass |
Print method for exponential objects.
Description
Print method for exponential objects.
Usage
## S3 method for class 'exponential'
print(x, ...)
Arguments
x |
The |
... |
Additional arguments (not used) |
Print the interval.
Description
Print the interval.
Usage
## S3 method for class 'interval'
print(x, ...)
Arguments
x |
An interval object. |
... |
Additional arguments. |
Method for printing an mvn object.
Description
Method for printing an mvn object.
Usage
## S3 method for class 'mvn'
print(x, ...)
Arguments
x |
The object to print |
... |
Additional arguments to pass to |
Method for printing a normal object.
Description
Method for printing a normal object.
Usage
## S3 method for class 'normal'
print(x, ...)
Arguments
x |
The object to print |
... |
Additional arguments to pass (not used) |
Print method for summary_dist objects.
Description
Print method for summary_dist objects.
Usage
## S3 method for class 'summary_dist'
print(x, ...)
Arguments
x |
The object to print |
... |
Additional arguments |
Generic method for applying a map f to distribution object x.
Description
Generic method for applying a map f to distribution object x.
Usage
rmap(x, g, ...)
Arguments
x |
The distribution object. |
g |
The function to apply. |
... |
Additional arguments to pass into |
Method for obtaining g(x)) where x is a dist object.
Description
We just sample from x and place the sample in empirical_dist and
then apply rmap with g to it.
Usage
## S3 method for class 'dist'
rmap(x, g, n = 10000L, ...)
Arguments
x |
The distribution object. |
g |
The function to apply to the distribution. |
n |
The number of samples to generate for the MC estimate of the conditional distribution x | P. Defaults to 10000. |
... |
additional arguments to pass into |
Method for obtaining the empirical distribution of a function of the
observations of empirical_dist object x.
Description
Method for obtaining the empirical distribution of a function of the
observations of empirical_dist object x.
Usage
## S3 method for class 'empirical_dist'
rmap(x, g, ...)
Arguments
x |
The empirical distribution object. |
g |
The function to apply to each observation. |
... |
Additional arguments to pass into function |
Computes the distribution of g(x) where x is an mvn object.
Description
By the invariance property, if x is an mvn object,
then under the right conditions, asymptotically, g(x) is an MVN
distributed,
g(x) ~ normal(g(mean(x)), sigma)
where sigma is the variance-covariance of g(x)
Usage
## S3 method for class 'mvn'
rmap(x, g, n = 10000L, ...)
Arguments
x |
The |
g |
The function to apply to |
n |
number of samples to take to estimate distribution of |
... |
additional arguments to pass into the |
Function for obtaining sample points for an mvn object that is within
the p-probability region. That is, it samples from the smallest region of
the distribution that contains p probability mass. This is done by first
sampling from the entire distribution, then rejecting samples that are not
in the probability region (using the statistical distance mahalanobis
from mu).
Description
Function for obtaining sample points for an mvn object that is within
the p-probability region. That is, it samples from the smallest region of
the distribution that contains p probability mass. This is done by first
sampling from the entire distribution, then rejecting samples that are not
in the probability region (using the statistical distance mahalanobis
from mu).
Usage
sample_mvn_region(n, mu, sigma, p = 0.95, ...)
Arguments
n |
the sample size |
mu |
mean vector |
sigma |
variance-covariance matrix |
p |
the probability region |
... |
additional arguments to pass into |
Generic method for sampling from distribution-like objects.
Description
It creates a sampler for the x object. It returns a function
that accepts a parameter n denoting the number of samples
to draw from the x object and also any additional parameters
... are passed to the generated function.
Usage
sampler(x, ...)
Arguments
x |
the |
... |
additional arguments to pass |
Sampler for non-dist objects (degenerate distributions).
Description
Sampler for non-dist objects (degenerate distributions).
Usage
## Default S3 method:
sampler(x, ...)
Arguments
x |
The object to sample from |
... |
Additional arguments to pass |
Value
A function that takes n and returns n copies of x
Method for obtaining the sampler of an edist object.
Description
Method for obtaining the sampler of an edist object.
Usage
## S3 method for class 'edist'
sampler(x, ...)
Arguments
x |
The |
... |
Additional arguments to pass into each of the |
Value
A function that takes a number of samples n, ...
which is passed into the expression x$e and returns
the result of applying the expression x$e to the
sampled values.
Method for obtaining the sampler for a empirical_dist object.
Description
Method for obtaining the sampler for a empirical_dist object.
Usage
## S3 method for class 'empirical_dist'
sampler(x, ...)
Arguments
x |
The object to obtain the sampler of. |
... |
Additional arguments to pass (not used). |
Method to sample from an exponential object.
Description
Method to sample from an exponential object.
Usage
## S3 method for class 'exponential'
sampler(x, ...)
Arguments
x |
The |
... |
Additional arguments to pass (not used) |
Value
A function that allows sampling from the exponential
distribution. Accepts an argument n denoting sample
size and rate denoting the failure rate. Defaults to
the failure rate of object x.
Function generator for sampling from a mvn (multivariate normal) object.
Description
Function generator for sampling from a mvn (multivariate normal) object.
Usage
## S3 method for class 'mvn'
sampler(x, ...)
Arguments
x |
The |
... |
Additional arguments to pass to the generated function that will be fixed during all calls. |
Value
A function that samples from the mvn distribution. It accepts as
input:
- n: number of samples to generate. Defaults to 1.
- mu: a vector denoting the population mean. Defaults to the mean
of x (an mvn object)
- sigma: a matrix denoting the covariance of observations.
Defaults to the variance-covariance of x.
- p: probability region to sample from. Defaults to 1, which
corresponds to the entire distribution.
sample_mvn_region method. It's used when p is less than 1.
- ...: any additional parameters to pass to rmvnorm or
sample_mvn_region which can be different during each call.
Method for sampling from a normal object.
Description
Method for sampling from a normal object.
Usage
## S3 method for class 'normal'
sampler(x, ...)
Arguments
x |
The |
... |
Additional arguments to pass (not used) |
Value
A function that samples from the normal distribution. As input,
it accepts a sample size n, a numeric mu, and a variance
numeric var. By default, mu and var are the mean and
variance of object x.
Generic method for simplifying distributions.
Description
Generic method for simplifying distributions.
Usage
simplify(x, ...)
Arguments
x |
The distribution to simplify |
... |
Additional arguments to pass |
Value
The simplified distribution
Default Method for simplifming a dist object. Just returns the object.
Description
Default Method for simplifming a dist object. Just returns the object.
Usage
## S3 method for class 'dist'
simplify(x, ...)
Arguments
x |
The |
... |
Additional arguments to pass (not used) |
Value
The dist object
Method for simplifying an edist object.
Description
Attempts to reduce expression distributions to closed-form distributions when mathematical identities apply. For example:
normal + normal = normal (sum of independent normals)
normal - normal = normal (difference of independent normals)
Usage
## S3 method for class 'edist'
simplify(x, ...)
Arguments
x |
The |
... |
Additional arguments to pass (not used) |
Value
The simplified distribution, or unchanged edist if no rule applies
Method for obtaining a summary of a dist object.
Description
Method for obtaining a summary of a dist object.
Usage
## S3 method for class 'dist'
summary(object, ..., name = NULL, nobs = NULL)
Arguments
object |
The object to obtain the summary of |
... |
Additional arguments to pass |
name |
The name of the distribution, defaults to the class of the object. |
nobs |
The number of observations to report for the summary, if applicable. |
Value
A summary_dist object
Method for constructing a summary_dist object.
Description
Method for constructing a summary_dist object.
Usage
summary_dist(name, mean, vcov, nobs = NULL)
Arguments
name |
The name of the distribution |
mean |
The mean of the distribution |
vcov |
The variance of the distribution |
nobs |
The number of observations used to construct the distribution, if applicable. |
Value
A summary_dist object
Generic method for retrieving the support of a (dist) object x.
Description
The returned value should have the following operations:
-
min: a vector, the minimum value of the support for each component. -
max: a vector, the maximum value of the support for each component. -
call: a predicate function, which returns TRUE if the value is in the support, and FALSE otherwise. -
sample: a function, which returns a sample from the support. Note that the returned value is not guaranteed to be in the support ofx. You may need to callcallto check.
Usage
sup(x)
Arguments
x |
The object to obtain the support of. |
Value
A support object for x.
Method for obtaining the support of empirical_dist object x.
Description
Method for obtaining the support of empirical_dist object x.
Usage
## S3 method for class 'empirical_dist'
sup(x)
Arguments
x |
The empirical distribution object. |
Value
A finite_set object containing the support of x.
Support for exponential distribution, the positive real numbers, (0, Inf).
Description
Support for exponential distribution, the positive real numbers, (0, Inf).
Usage
## S3 method for class 'exponential'
sup(x)
Arguments
x |
The object to obtain the support of |
Value
An interval object representing the support of the exponential
Method for obtaining the support of a mvn object, where the support
is defined as values that have non-zero probability density.
Description
Method for obtaining the support of a mvn object, where the support
is defined as values that have non-zero probability density.
Usage
## S3 method for class 'mvn'
sup(x, ...)
Arguments
x |
The |
... |
Additional arguments to pass (not used) |
Value
A support-type object (see support.R), in this case an
interval object for each component.
Method for obtaining the support of a normal object, where the support
is defined as values that have non-zero probability density.
Description
Method for obtaining the support of a normal object, where the support
is defined as values that have non-zero probability density.
Usage
## S3 method for class 'normal'
sup(x)
Arguments
x |
The |
Value
A support-type object (see support.R), in this case an
interval object for each component.
Get the supremum of the support.
Description
Get the supremum of the support.
Usage
supremum(object)
Arguments
object |
A support object. |
Return the supremum of the finite set.
Description
Return the supremum of the finite set.
Usage
## S3 method for class 'finite_set'
supremum(object)
Arguments
object |
A finite set. |
Return the (vector of) supremum of the interval.
Description
Return the (vector of) supremum of the interval.
Usage
## S3 method for class 'interval'
supremum(object)
Arguments
object |
An interval object. |
Generic method for obtaining the survival function of an object.
Description
Generic method for obtaining the survival function of an object.
Usage
surv(x, ...)
Arguments
x |
The object to obtain the survival function of. |
... |
Additional arguments to pass. |
Method to obtain the cdf of an exponential object.
Description
Method to obtain the cdf of an exponential object.
Usage
## S3 method for class 'exponential'
surv(x, ...)
Arguments
x |
The object to obtain the pdf of |
... |
Additional arguments (not used) |
Value
A function that computes the cdf of the exponential. Accepts as
input a vector t at which to compute the cdf, an input rate
denoting the failure rate of the exponential distribution, and a
logical log indicating whether to compute the log of the cdf.
By default, rate is the failure rate of object x.
Variance-covariance for non-dist objects (degenerate distributions).
Description
Variance-covariance for non-dist objects (degenerate distributions).
Usage
## Default S3 method:
vcov(object, ...)
Arguments
object |
The object (returns 0 for constants) |
... |
Additional arguments to pass (not used) |
Value
0 (degenerate distributions have no variance)
Method for obtaining the variance-covariance matrix (or scalar)
Description
Method for obtaining the variance-covariance matrix (or scalar)
Usage
## S3 method for class 'edist'
vcov(object, n = 10000, ...)
Arguments
object |
The |
n |
The number of samples to take (default: 1000) |
... |
Additional arguments to pass (not used) |
Value
The variance-covariance matrix of the edist object
Method for obtaining the variance of empirical_dist object x.
Description
Method for obtaining the variance of empirical_dist object x.
Usage
## S3 method for class 'empirical_dist'
vcov(object, ...)
Arguments
object |
The empirical distribution object. |
... |
Additional arguments to pass (not used). |
Retrieve the variance of a exponential object.
Description
Retrieve the variance of a exponential object.
Usage
## S3 method for class 'exponential'
vcov(object, ...)
Arguments
object |
The |
... |
Additional arguments to pass (not used) |
Value
The variance-covariance matrix of the normal object
Retrieve the variance-covariance matrix of an mvn object.
Description
Retrieve the variance-covariance matrix of an mvn object.
Usage
## S3 method for class 'mvn'
vcov(object, ...)
Arguments
object |
The |
... |
Additional arguments to pass (not used) |
Value
The variance-covariance matrix of the mvn object
Retrieve the variance-covariance matrix (or scalar)
of a normal object.
Description
Retrieve the variance-covariance matrix (or scalar)
of a normal object.
Usage
## S3 method for class 'normal'
vcov(object, ...)
Arguments
object |
The |
... |
Additional arguments to pass (not used) |
Value
The variance-covariance matrix of the normal object
Method for obtaining the variance of univariate_dist object.
Description
Method for obtaining the variance of univariate_dist object.
Usage
## S3 method for class 'univariate_dist'
vcov(object, ...)
Arguments
object |
The distribution object. |
... |
Additional arguments to pass into |