R: Algebra over Probability Distributions

# Algebra over Probability Distributions

## Documentation for package ‘algebraic.dist’ version 1.0.0

- DESCRIPTION file
- User guides, package vignettes and other documentation
- Package NEWS
- Package README

## Help Pages

A B C D E F G H I L M N O P R S U V W misc

## -- A --

affine_transform | Affine transformation of a normal or multivariate normal distribution.
as_dist | Convert an object to a probability distribution.
as_dist.dist | Convert an object to a probability distribution.

## -- B --

beta_dist | Construct a beta distribution object.

## -- C --

cdf | Generic method for obtaining the cdf of an object.
cdf.beta_dist | Cumulative distribution function for a beta distribution.
cdf.chi_squared | Method for obtaining the cdf of a 'chi_squared' object.
cdf.edist | CDF for expression distributions.
cdf.empirical_dist | Method for obtaining the cdf of 'empirical_dist' object 'x'.
cdf.exponential | Method to obtain the cdf of an 'exponential' object.
cdf.gamma_dist | Method for obtaining the cdf of a 'gamma_dist' object.
cdf.lognormal | Cumulative distribution function for a log-normal distribution.
cdf.mixture | Cumulative distribution function for a mixture distribution.
cdf.mvn | Method for obtaining the CDF of a 'mvn' object.
cdf.normal | Method for obtaining the cdf of an 'normal' object.
cdf.poisson_dist | Cumulative distribution function for a Poisson distribution.
cdf.uniform_dist | Cumulative distribution function for a uniform distribution.
cdf.weibull_dist | Cumulative distribution function for a Weibull distribution.
chi_squared | Construct a chi-squared distribution object.
clt | Central Limit Theorem Limiting Distribution
conditional | Generic method for obtaining the conditional distribution of a distribution object 'x' given condition 'P'.
conditional.dist | Method for obtaining the condition distribution, 'x | P(x)', of 'dist' object 'x'.
conditional.edist | Conditional distribution for expression distributions.
conditional.empirical_dist | Method for obtaining the condition distribution, 'x | P(x)', of 'empirical_dist' object 'x'.
conditional.mixture | Conditional distribution of a mixture.
conditional.mvn | Conditional distribution for multivariate normal.
countable_set | Countable Set

## -- D --

delta_clt | Delta Method CLT Limiting Distribution
density.beta_dist | Probability density function for a beta distribution.
density.chi_squared | Method for obtaining the density (pdf) of a 'chi_squared' object.
density.edist | Density for expression distributions.
density.empirical_dist | Method for obtaining the pdf of a 'empirical_dist' object.
density.exponential | Method to obtain the pdf of an 'exponential' object.
density.gamma_dist | Method for obtaining the density (pdf) of a 'gamma_dist' object.
density.lognormal | Probability density function for a log-normal distribution.
density.mixture | Probability density function for a mixture distribution.
density.mvn | Function generator for obtaining the pdf of an 'mvn' object (multivariate normal).
density.normal | Method for obtaining the pdf of an 'normal' object.
density.poisson_dist | Probability mass function for a Poisson distribution.
density.uniform_dist | Probability density function for a uniform distribution.
density.weibull_dist | Probability density function for a Weibull distribution.
dim.beta_dist | Dimension of a beta distribution (always 1).
dim.chi_squared | Retrieve the dimension of a 'chi_squared' object.
dim.countable_set | Get the dimension of a countable set.
dim.edist | Method for obtaining the dimension of an 'edist' object.
dim.empirical_dist | Method for obtaining the dimension of a 'empirical_dist' object.
dim.exponential | Method to obtain the dimension of an 'exponential' object.
dim.finite_set | Return the dimension of the finite set.
dim.gamma_dist | Retrieve the dimension of a 'gamma_dist' object.
dim.interval | Return the dimension of the interval.
dim.lognormal | Dimension of a log-normal distribution (always 1).
dim.mixture | Dimension of a mixture distribution.
dim.mvn | Method for obtaining the dimension of an 'mvn' object.
dim.normal | Method for obtaining the dimension of a 'normal' object.
dim.poisson_dist | Dimension of a Poisson distribution (always 1).
dim.uniform_dist | Dimension of a uniform distribution (always 1).
dim.weibull_dist | Dimension of a Weibull distribution (always 1).

## -- E --

edist | 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.
empirical_dist | Construct empirical distribution object.
expectation | Generic method for obtaining the expectation of 'f' with respect to 'x'.
expectation.dist | Expectation of a Function Applied to a 'dist' Object
expectation.empirical_dist | Method for obtaining the expectation of 'empirical_dist' object 'x' under function 'g'.
expectation.poisson_dist | Exact expectation for a Poisson distribution.
expectation.univariate_dist | Method for obtaining the expectation of 'f' with respect to a 'univariate_dist' object 'x'.
expectation_data | 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.
exponential | Construct exponential distribution object.

## -- F --

finite_set | Finite set
format.beta_dist | Format a 'beta_dist' object as a character string.
format.chi_squared | Format a 'chi_squared' object as a character string.
format.edist | Format method for 'edist' objects.
format.empirical_dist | Format method for 'empirical_dist' objects.
format.exponential | Format method for 'exponential' objects.
format.gamma_dist | Format a 'gamma_dist' object as a character string.
format.lognormal | Format a 'lognormal' object as a character string.
format.mixture | Format a 'mixture' object as a character string.
format.mvn | Format method for 'mvn' objects.
format.normal | Format method for 'normal' objects.
format.poisson_dist | Format a 'poisson_dist' object as a character string.
format.realized_dist | Format a 'realized_dist' object as a character string.
format.uniform_dist | Format a 'uniform_dist' object as a character string.
format.weibull_dist | Format a 'weibull_dist' object as a character string.

## -- G --

gamma_dist | Construct a gamma distribution object.

## -- H --

has | Support
has.countable_set | Check membership in a countable set.
has.finite_set | Determine if a value is contained in the finite set.
has.interval | Determine if a value is contained in the interval.
hazard | Default hazard function for continuous distributions.
hazard.chi_squared | Method for obtaining the hazard function of a 'chi_squared' object.
hazard.continuous_dist | Default hazard function for continuous distributions.
hazard.exponential | Method to obtain the hazard function of an 'exponential' object.
hazard.gamma_dist | Method for obtaining the hazard function of a 'gamma_dist' object.
hazard.lognormal | Hazard function for a log-normal distribution.
hazard.weibull_dist | Hazard function for a Weibull distribution.

## -- I --

infimum | Get the infimum of the support.
infimum.countable_set | Get the infimum of a countable set.
infimum.finite_set | Return the infimum of the finite set.
infimum.interval | Return the (vector of) infimum of the interval.
interval | Interval
inv_cdf | Generic method for obtaining the quantile (inverse cdf) of an object.
inv_cdf.beta_dist | Inverse CDF (quantile function) for a beta distribution.
inv_cdf.chi_squared | Method for obtaining the inverse cdf (quantile function) of a 'chi_squared' object.
inv_cdf.edist | Inverse CDF (quantile function) for expression distributions.
inv_cdf.empirical_dist | Method for obtaining the inverse CDF (quantile function) of a univariate 'empirical_dist' object.
inv_cdf.exponential | Method to obtain the inverse cdf of an 'exponential' object.
inv_cdf.gamma_dist | Method for obtaining the inverse cdf (quantile function) of a 'gamma_dist' object.
inv_cdf.lognormal | Inverse CDF (quantile function) for a log-normal distribution.
inv_cdf.normal | Method for obtaining the inverse cdf of an 'normal' object.
inv_cdf.poisson_dist | Inverse CDF (quantile function) for a Poisson distribution.
inv_cdf.uniform_dist | Inverse CDF (quantile function) for a uniform distribution.
inv_cdf.weibull_dist | Inverse CDF (quantile function) for a Weibull distribution.
is_beta_dist | Test whether an object is a 'beta_dist'.
is_chi_squared | Test whether an object is a 'chi_squared'.
is_dist | Function to determine whether an object 'x' is a 'dist' object.
is_edist | Function to determine whether an object 'x' is an 'edist' object.
is_empirical_dist | Function to determine whether an object 'x' is an 'empirical_dist' object.
is_exponential | Function to determine whether an object 'x' is an 'exponential' object.
is_gamma_dist | Test whether an object is a 'gamma_dist'.
is_lognormal | Test whether an object is a 'lognormal'.
is_mixture | Test whether an object is a 'mixture' distribution.
is_mvn | Function to determine whether an object 'x' is an 'mvn' object.
is_normal | Function to determine whether an object 'x' is an 'normal' object.
is_poisson_dist | Test whether an object is a 'poisson_dist'.
is_realized_dist | Test whether an object is a 'realized_dist'.
is_uniform_dist | Test whether an object is a 'uniform_dist'.
is_weibull_dist | Test whether an object is a 'weibull_dist'.

## -- L --

lln | Law of Large Numbers Limiting Distribution
lognormal | Construct a log-normal distribution object.

## -- M --

marginal | Generic method for obtaining the marginal distribution of a distribution object 'x' over components 'indices'.
marginal.empirical_dist | Method for obtaining the marginal distribution of 'empirical_dist' object 'x'.
marginal.mixture | Marginal distribution of a mixture.
marginal.mvn | Generic method for obtaining the marginal distribution of an 'mvn' object 'x' over components 'indices'.
Math.dist | Math group generic for distribution objects.
mean.beta_dist | Mean of a beta distribution.
mean.chi_squared | Retrieve the mean of a 'chi_squared' object.
mean.edist | Method for obtaining the mean of an 'edist' object.
mean.empirical_dist | Method for obtaining the mean of 'empirical_dist' object 'x'.
mean.exponential | Method to obtain the mean of an 'exponential' object.
mean.gamma_dist | Retrieve the mean of a 'gamma_dist' object.
mean.lognormal | Mean of a log-normal distribution.
mean.mixture | Mean of a mixture distribution.
mean.mvn | Retrieve the mean of a 'mvn' object.
mean.normal | Retrieve the mean of a 'normal' object.
mean.poisson_dist | Mean of a Poisson distribution.
mean.uniform_dist | Mean of a uniform distribution.
mean.univariate_dist | Method for obtaining the mean of 'univariate_dist' object 'x'.
mean.weibull_dist | Mean of a Weibull distribution.
mixture | Construct a mixture distribution.
mvn | Construct a multivariate or univariate normal distribution object.

## -- N --

nobs.empirical_dist | Method for obtaining the number of observations used to construct a 'empirical_dist' object.
normal | Construct univariate normal distribution object.
normal_approx | Moment-Matching Normal Approximation
nparams | Generic method for obtaining the number of parameters of distribution-like object 'x'.
nparams.dist | Generic method for obtaining the number of parameters of distribution-like object 'x'.
nparams.empirical_dist | Method for obtaining the name of a 'empirical_dist' object. Since the empirical distribution is parameter-free, this function returns 0.
nparams.mixture | Number of parameters for a 'mixture' distribution.

## -- O --

obs | 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.
obs.empirical_dist | Method for obtaining the observations used to construct a 'empirical_dist' object.

## -- P --

params | Generic method for obtaining the parameters of an object.
params.beta_dist | Retrieve the parameters of a 'beta_dist' object.
params.chi_squared | Method for obtaining the parameters of a 'chi_squared' object.
params.edist | Method for obtaining the parameters of an 'edist' object.
params.empirical_dist | 'empirical_dist' objects have no parameters, so this function returns NULL.
params.exponential | Method for obtaining the parameters of an 'exponential' object.
params.gamma_dist | Method for obtaining the parameters of a 'gamma_dist' object.
params.lognormal | Retrieve the parameters of a 'lognormal' object.
params.mixture | Retrieve the parameters of a 'mixture' object.
params.mvn | Method for obtaining the parameters of a 'mvn' object.
params.normal | Method for obtaining the parameters of a 'normal' object.
params.poisson_dist | Retrieve the parameters of a 'poisson_dist' object.
params.uniform_dist | Retrieve the parameters of a 'uniform_dist' object.
params.weibull_dist | Retrieve the parameters of a 'weibull_dist' object.
poisson_dist | Construct a Poisson distribution object.
print.beta_dist | Print a 'beta_dist' object.
print.chi_squared | Print method for 'chi_squared' objects.
print.edist | Print method for 'edist' objects.
print.empirical_dist | Print method for 'empirical_dist' objects.
print.exponential | Print method for 'exponential' objects.
print.gamma_dist | Print method for 'gamma_dist' objects.
print.interval | Print the interval.
print.lognormal | Print a 'lognormal' object.
print.mixture | Print a 'mixture' object.
print.mvn | Method for printing an 'mvn' object.
print.normal | Print method for 'normal' objects.
print.poisson_dist | Print a 'poisson_dist' object.
print.realized_dist | Print a 'realized_dist' object.
print.summary_dist | Print method for 'summary_dist' objects.
print.uniform_dist | Print a 'uniform_dist' object.
print.weibull_dist | Print a 'weibull_dist' object.

## -- R --

realize | Materialize any distribution to empirical_dist by sampling.
realize.dist | Materialize any distribution to empirical_dist by sampling.
realize.empirical_dist | Materialize any distribution to empirical_dist by sampling.
realize.realized_dist | Materialize any distribution to empirical_dist by sampling.
rmap | Generic method for applying a map 'f' to distribution object 'x'.
rmap.dist | Method for obtaining g(x)) where x is a 'dist' object.
rmap.edist | Map function over expression distribution.
rmap.empirical_dist | Method for obtaining the empirical distribution of a function of the observations of 'empirical_dist' object 'x'.
rmap.mvn | Computes the distribution of 'g(x)' where 'x' is an 'mvn' object.

## -- S --

sampler | Generic method for sampling from distribution-like objects.
sampler.beta_dist | Sampler for a beta distribution.
sampler.chi_squared | Method for sampling from a 'chi_squared' object.
sampler.default | Sampler for non-dist objects (degenerate distributions).
sampler.edist | Method for obtaining the sampler of an 'edist' object.
sampler.empirical_dist | Method for obtaining the sampler for a 'empirical_dist' object.
sampler.exponential | Method to sample from an 'exponential' object.
sampler.gamma_dist | Method for sampling from a 'gamma_dist' object.
sampler.lognormal | Sampler for a log-normal distribution.
sampler.mixture | Sampler for a mixture distribution.
sampler.mvn | Function generator for sampling from a 'mvn' (multivariate normal) object.
sampler.normal | Method for sampling from a 'normal' object.
sampler.poisson_dist | Sampler for a Poisson distribution.
sampler.uniform_dist | Sampler for a uniform distribution.
sampler.weibull_dist | Sampler for a Weibull distribution.
sample_mvn_region | 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').
simplify | Generic method for simplifying distributions.
simplify.dist | Default Method for simplifying a 'dist' object. Just returns the object.
simplify.edist | Method for simplifying an 'edist' object.
Summary.dist | Summary group generic for distribution objects.
summary.dist | Method for obtaining a summary of a 'dist' object.
summary_dist | Method for constructing a 'summary_dist' object.
sup | Generic method for retrieving the support of a (dist) object 'x'.
sup.beta_dist | Support of a beta distribution.
sup.chi_squared | Support for chi-squared distribution, the positive real numbers (0, Inf).
sup.edist | Support for expression distributions.
sup.empirical_dist | Method for obtaining the support of 'empirical_dist' object 'x'.
sup.exponential | Support for exponential distribution, the positive real numbers, (0, Inf).
sup.gamma_dist | Support for gamma distribution, the positive real numbers (0, Inf).
sup.lognormal | Support of a log-normal distribution.
sup.mixture | Support of a mixture distribution.
sup.mvn | Method for obtaining the support of a 'mvn' object, where the support is defined as values that have non-zero probability density.
sup.normal | Method for obtaining the support of a 'normal' object, where the support is defined as values that have non-zero probability density.
sup.poisson_dist | Support of a Poisson distribution.
sup.uniform_dist | Support of a uniform distribution.
sup.weibull_dist | Support of a Weibull distribution.
supremum | Get the supremum of the support.
supremum.countable_set | Get the supremum of a countable set.
supremum.finite_set | Return the supremum of the finite set.
supremum.interval | Return the (vector of) supremum of the interval.
surv | Default survival function for continuous distributions.
surv.chi_squared | Method for obtaining the survival function of a 'chi_squared' object.
surv.continuous_dist | Default survival function for continuous distributions.
surv.exponential | Method to obtain the survival function of an 'exponential' object.
surv.gamma_dist | Method for obtaining the survival function of a 'gamma_dist' object.
surv.lognormal | Survival function for a log-normal distribution.
surv.weibull_dist | Survival function for a Weibull distribution.

## -- U --

uniform_dist | Construct a uniform distribution object.

## -- V --

vcov.beta_dist | Variance of a beta distribution.
vcov.chi_squared | Retrieve the variance of a 'chi_squared' object.
vcov.default | Variance-covariance for non-dist objects (degenerate distributions).
vcov.edist | Method for obtaining the variance-covariance matrix (or scalar)
vcov.empirical_dist | Method for obtaining the variance of 'empirical_dist' object 'x'.
vcov.exponential | Retrieve the variance of a 'exponential' object.
vcov.gamma_dist | Retrieve the variance of a 'gamma_dist' object.
vcov.lognormal | Variance of a log-normal distribution.
vcov.mixture | Variance of a mixture distribution.
vcov.mvn | Retrieve the variance-covariance matrix of an 'mvn' object.
vcov.normal | Retrieve the variance-covariance matrix (or scalar) of a 'normal' object.
vcov.poisson_dist | Variance of a Poisson distribution.
vcov.uniform_dist | Variance of a uniform distribution.
vcov.univariate_dist | Method for obtaining the variance of 'univariate_dist' object.
vcov.weibull_dist | Variance of a Weibull distribution.

## -- W --

weibull_dist | Construct a Weibull distribution object.

## -- misc --

*.dist | Multiplication of distribution objects.
+.dist | Method for adding 'dist' objects, or shifting a distribution by a scalar.
-.dist | Method for negation or subtraction of 'dist' objects.
/.dist | Division of distribution objects.
^.dist | Power operator for distribution objects.