Algebra over Probability Distributions

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Documentation for package ‘algebraic.dist’ version 0.1.0

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C D E F H I M N O P R S V misc

-- C --

cdf Generic method for obtaining the cdf of an object.
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.mvn Method for obtaining the CDF of a 'mvn' object.
cdf.normal Method for obtaining the cdf of an 'normal' object.
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.empirical_dist Method for obtaining the condition distribution, 'x | P(x)', of 'empirical_dist' object 'x'.

-- D --

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.mvn Function generator for obtaining the pdf of an 'mvn' object (multivariate normal).
density.normal Method for obtaining the pdf of an 'normal' 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.interval Return the dimension of the interval.
dim.mvn Method for obtaining the dimension of an 'mvn' object.
dim.normal Method for obtaining the dimension of a 'normal' object.

-- 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.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

-- H --

has Support
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.exponential Method to obtain the hazard function of an 'exponential' object.

-- I --

infimum Get the infimum of the support.
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.exponential Method to obtain the inverse cdf of an 'exponential' object.
inv_cdf.normal Method for obtaining the inverse cdf of an 'normal' object.
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_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.

-- 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.mvn Generic method for obtaining the marginal distribution of an 'mvn' object 'x' over components 'indices'.
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.mvn Retrieve the mean of a 'mvn' object.
mean.normal Retrieve the mean of a 'normal' object.
mean.univariate_dist Method for obtaining the mean of 'univariate_dist' object 'x'.
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.
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.

-- 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.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.mvn Method for obtaining the parameters of a 'mvn' object.
params.normal Method for obtaining the parameters of a 'normal' object.
print.edist Method for printing an 'edist' object.
print.empirical_dist Method for printing a 'dist' object
print.exponential Print method for 'exponential' objects.
print.interval Print the interval.
print.mvn Method for printing an 'mvn' object.
print.normal Method for printing a 'normal' object.
print.summary_dist Print method for 'summary_dist' objects.

-- R --

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.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.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.mvn Function generator for sampling from a 'mvn' (multivariate normal) object.
sampler.normal Method for sampling from a 'normal' object.
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 simplifming a 'dist' object. Just returns the object.
simplify.edist Method for simplifying an 'edist' object.
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.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.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.
supremum Get the supremum of the support.
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.exponential Method to obtain the cdf of an 'exponential' object.

-- V --

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.mvn Retrieve the variance-covariance matrix of an 'mvn' object.
vcov.normal Retrieve the variance-covariance matrix (or scalar) of a 'normal' object.
vcov.univariate_dist Method for obtaining the variance of 'univariate_dist' object.

-- misc --

+.dist Method for adding 'dist' objects.
-.dist Method for negation or subtraction of 'dist' objects.