Algebra over Probability Distributions

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Documentation for package ‘algebraic.dist’ version 0.9.1

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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.