Algebra over Probability Distributions

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Documentation for package ‘algebraic.dist’ version 0.9.1

• DESCRIPTION file.
• User guides, package vignettes and other documentation.
• Package NEWS.

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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.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	Generic method for obtaining the hazard function of an object.
hazard.chi_squared	Method for obtaining the hazard function of a 'chi_squared' object.
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.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	Generic method for obtaining the survival function of an object.
surv.chi_squared	Method for obtaining the survival function of a 'chi_squared' object.
surv.exponential	Method to obtain the cdf 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.