Package 'distributions' reference manual

Title:	What the Package Does (Title Case)
Description:	More about what it does (maybe more than one line) Use four spaces when indenting paragraphs within the Description.
Authors:	Who wrote it
Maintainer:	The package maintainer <[email protected]>
License:	What license is it under?
Version:	1.0.0
Built:	2026-11-13 19:00:31 UTC
Source:	https://github.com/tfojo1/distributions

Create a multivariate normal distribution with a Continuous Autoregressive 1 (CAR-1) correlation structure

Description

Creates a distribution where all the variables, after arbitrary transformations, follow a normal distribution with a Continuous Autoregressive 1 (CAR-1) correlation structure

Usage

Autoregressive.Multivariate.Normal.Distribution(
  rho,
  times,
  mu = 0,
  sds = 1,
  lower = -Inf,
  upper = Inf,
  var.names = NULL,
  transformations = NULL
)
Autoregressive.Multivariate.Normal.Distribution(
  rho,
  times,
  mu = 0,
  sds = 1,
  lower = -Inf,
  upper = Inf,
  var.names = NULL,
  transformations = NULL
)

Arguments

rho

The autoregressive correlation coefficient

times

The times for each observation in the distribution. The correlation between any two observations at times t1 and t2 is rho^(abs(t1-t2))

mu, sds

The mean and standard deviation vectors. If given a scalar value, assumes that the mean/sd is the same for every variable in the distribution

lower

The upper and lower bounds for each variable (on the original scale, NOT the transformed scale). If only one value is given, assumed to apply to all variables in the distribution

upper

The upper and lower bounds for each variable (on the original scale, NOT the transformed scale). If only one value is given, assumed to apply to all variables in the distribution

var.names

The names of the variables in the distribution. If NULL, uses the names of mu, the row names of sigma, or the column names of sigma, in that order

transformations

Objects of class transformation to be applied to each variable. Can be either an object of class transformation, the character name of a defined transformation, or a list of transformation objects. If only one transformation is supplied, assumed to apply to all variables. If this is a named list, any variables missing transformation are assmed to not be transformed

Create a Univariate Bernoulli Distribution Object

Description

Create a Univariate Bernoulli Distribution Object

Usage

Bernoulli.Distribution(p = 0.5, var.name = NULL)
Bernoulli.Distribution(p = 0.5, var.name = NULL)

Arguments

p

The probability of success in the distribution

var.name

The name of the single variable in the distribution, or NULL if no name is specified

Create a Univariate Beta Distribution Object

Description

Create a Univariate Beta Distribution Object

Usage

Beta.Distribution(alpha = 1, beta = 1, lower = 0, upper = 1, var.name = NULL)
Beta.Distribution(alpha = 1, beta = 1, lower = 0, upper = 1, var.name = NULL)

Arguments

alpha, beta

The parameters to the beta distribution (AKA shape1, shape2 respectively in dbeta)

lower, upper

The lower and the upper bounds

var.name

The name of the single variable in the distribution, or NULL if no name is specified

Create a Univariate Binomial Distribution Object

Description

Create a Univariate Binomial Distribution Object

Usage

Binomial.Distribution(n = 10, p = 0.5, lower = 0, upper = n, var.name = NULL)
Binomial.Distribution(n = 10, p = 0.5, lower = 0, upper = n, var.name = NULL)

Arguments

n, p

The size and probability parameters to the distribution (AKA size, prob in dbinom)

lower, upper

The lower and the upper bounds

var.name

The name of the single variable in the distribution, or NULL if no name is specified

Calculate the cumulative distribution function for a distribution

Description

Calculate the cumulative distribution function for a distribution

Usage

calculate.cdf(dist, q, lower.tail = T, log.p = F, n.sim = 1000 * [email protected])
calculate.cdf(dist, q, lower.tail = T, log.p = F, n.sim = 1000 * dist@n.var)

Arguments

dist

An object of class Distribution or a subclass

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

x

The values of the parameters at which to calculate the CDF. May be either a vector, if the CDF at a single point is desired, or a matrix where each row represents one point and each column represents a variable in the distribution

log

A logical indicating whether to return the CDF on the log scale

Details

Note to developers: this function should not be overridden. Override do.calculate.cdf instead

Value

If x is a vector, a scalar density. If x is a matrix, a numeric vector of densities, one for each row in x

Calculate a marginal cumulative distribution function for each variable in a distribution

Description

Calculate a marginal cumulative distribution function for each variable in a distribution

Usage

calculate.marginal.cdfs(dist, q, lower.tail = T, log.p = F, n.sim = 1000)
calculate.marginal.cdfs(dist, q, lower.tail = T, log.p = F, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

Note to developers: this function should not be overridden. Override do.calculate.marginal.cdfs instead

Value

If q is a vector, a vector of probabilities with one value for each variable in the distribution. If q is a matrix, a matrix of probabilites, with one for each row in x and one column for each variable in the distribution

Calculate a marginal density for each variable in a distribution

Description

Calculate a marginal density for each variable in a distribution

Usage

calculate.marginal.densities(dist, x, log = F, n.sim = 1000)
calculate.marginal.densities(dist, x, log = F, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

x

The values of the parameters at which to calculate the density. May be either a vector, if the density at a single point is desired, or a matrix where each row represents one point and each column represents a variable in the distribution

log

A logical indicating whether to return the density on the log scale

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

Note to developers: this function should not be overridden. Override do.calculate.marginal.densities instead

Value

If x is a vector or a matrix with only one row, a vector of densities with one value for each variable in the distribution. If x is a matrix, a matrix of densities, with one for each row in x and one column for each variable in the distribution

The Canonical_Mixture_Distribution class

Description

A class that represents a univariate mixture of different instances of a canonical distribution (the same distribution, but with different parameters)

Slots

name: A short, descriptive name for the distribution
n.components: The number of component distributions in this mixture
weights: The weights for the component distributions in the mixture (sum(weights)=1)
density.function.name,cdf.function.name,quantile.function.name: Names of the (elsewhere defined) functions that calculate density, cdf, and quantiles (eg 'dnorm', 'pnorm', and 'qnorm)
parameters: A list of vectors; each element of the list represents a parameter to the distribution, and the values of the vector represent the parameter values for each component of the mixture
p.in.bounds,log.p.in.bounds: A vector cumulative probabilities and of the log cumulative probabilities between the lower and upper bounds for each component of the mixture
p.lower.bound: A vector of values of the cdf evaluated at the lower bound for each components of the distribution
transformation: An object of class transformation, defining the transformation applied to the variable before applying the distribution (eg, )
means,variances: If known, the means and variances of each component of the distribution. May be NA

Create a mixture distribution object based off of a canonical, univariate distribution

Usage

Canonical.Mixture.Distribution(
  name,
  dist.name,
  parameters,
  weights = 1,
  var.name = NULL,
  support = Continuous.Support(),
  density.function.name = paste0("d", dist.name),
  cdf.function.name = paste0("p", dist.name),
  quantile.function.name = paste0("q", dist.name),
  transformation = NULL,
  is.improper = F,
  mean.values = as.numeric(NA),
  variance.values = as.numeric(NA)
)
Canonical.Mixture.Distribution(
  name,
  dist.name,
  parameters,
  weights = 1,
  var.name = NULL,
  support = Continuous.Support(),
  density.function.name = paste0("d", dist.name),
  cdf.function.name = paste0("p", dist.name),
  quantile.function.name = paste0("q", dist.name),
  transformation = NULL,
  is.improper = F,
  mean.values = as.numeric(NA),
  variance.values = as.numeric(NA)
)

Arguments

name

A short, descriptive name for the distribution

dist.name

The root name of the distribution as used by d/r/p functions in R. For example, to create a normal distribution, dist.name='norm' (like dnorm, rnorm, pnorm). To create a beta distribution, dist.name='beta' (dbeta, rbeta, qbeta). This argument is only necessary if density.function, cdf.function, and quantile.function are not passed explicitly

parameters

A list of vectors, where each element has parameter values that would be passed to d/r/p functions in R. For example, for a mixture of normal(0,1) and normal(1,1) distributions, parameters=list(mean=c(0,1), sd=1) or parameters=list(mean=c(0,1), sd=c(1,1))

weights

A weight for each component distribution in the mixture. The weights need not sum to 1. If a scalar is passed, all components are given the same weight

var.name

The name of the variable in this distribution

transformation

A transformation object, if the named distribution operates on a transformation of the random variable (can also pass NULL for no transformation or the name of a predefined transformation - see get.defined.transformation). For example, to create a log-normal distribution, use dist.name='norm' with transformation='log

is.improper, is.discrete

Logicals indicating whether the distribution is improper/discrete

mean.values, variance.values

If known, vectors of values for the means and variances of each component of the distribution

lower.bound, upper.bound

If this is a bounded distribution, the lower and upper bounds

density.function, cdf.function, quantile.function

The functions that calculate the density, cdf, and quantile respectively. These should take the standard parameters of such functions in R. density.function should take 'x', distribution-specific parameters, and 'log'. cdf.function should take 'q', distribution-specific parameters, 'lower.tail' and 'log.p'. quantile.function should take 'p', distribution-specific parameters, and 'lower.tail' and 'log.p'

Create a multivariate normal distribution with a Compound Symmetry correlation structure

Description

Creates a distribution where all the variables, after arbitrary transformations, follow a normal distribution with a Compound Symmetry (AKA Exchangeable) correlation structure

Usage

Compound.Symmetry.Multivariate.Normal.Distribution(
  rho,
  n = max(length(mu), length(sds)),
  mu = 0,
  sds = 1,
  lower = -Inf,
  upper = Inf,
  var.names = NULL,
  transformations = NULL
)
Compound.Symmetry.Multivariate.Normal.Distribution(
  rho,
  n = max(length(mu), length(sds)),
  mu = 0,
  sds = 1,
  lower = -Inf,
  upper = Inf,
  var.names = NULL,
  transformations = NULL
)

Arguments

rho

The correlation coefficient

n

The number of variables in the distribution

mu, sds

The mean and standard deviation vectors. If given a scalar value, assumes that the mean/sd is the same for every variable in the distribution

lower

The upper and lower bounds for each variable (on the original scale, NOT the transformed scale). If only one value is given, assumed to apply to all variables in the distribution

upper

The upper and lower bounds for each variable (on the original scale, NOT the transformed scale). If only one value is given, assumed to apply to all variables in the distribution

var.names

The names of the variables in the distribution. If NULL, uses the names of mu, the row names of sigma, or the column names of sigma, in that order

transformations

The Constant_Distribution class

Description

A class that represents a probility distribution with support for exactly one value

Slots

value: The single value supported by this distribution

Create a distribution representing a Constant Distribution

Description

Creates an object representing a degenerate distribution that only supports a single, discrete value

Usage

Constant.Distribution(value, var.name = NULL)
Constant.Distribution(value, var.name = NULL)

Arguments

value

The single value supported by the distribution

var.name

The name of the single variable in the distribution, or NULL if no name is specified

Create an object which represents support over a range of integers

Description

Create an object which represents support over a range of integers

Usage

Continuous.Support(
  lower = -Inf,
  upper = Inf,
  lower.inclusive = F,
  upper.inclusive = F
)
Continuous.Support(
  lower = -Inf,
  upper = Inf,
  lower.inclusive = F,
  upper.inclusive = F
)

Arguments

lower, upper

The lower and upper bounds of support. For a single range of support, these should both be of length 1. If support exists over multiple disjoint ranges, then lower and upper should be numeric vectors of the same length, with the lower and upper bounds of each of the disjoint ranges

lower.inclusive, upper.inclusive

Logical vectors indicating whether the lower and upper bounds are inclusive (vs. exclusive). If length(lower)/length(upper) are >1, these can be either logical vectors of the same length, or logical scalars (in which case the value applies to each element of lower and upper)

Value

An object of class Range_Support, such that is.supported is true if x falls within any of the ranges lower[i] to upper[i]

Create an object representing a transformation

Description

Create an object representing a transformation

Usage

create.transformation(
  transform.function,
  reverse.transform.function,
  transformation.derivative,
  log.abs.transformation.derivative = NULL,
  name
)
create.transformation(
  transform.function,
  reverse.transform.function,
  transformation.derivative,
  log.abs.transformation.derivative = NULL,
  name
)

Arguments

transform.function, reverse.transform.function, transformation.derivative, log.transformation.derivative

Functions that compute the transformation, inverse transformation, derivative of the transformation function, and log of the derivative of the transformation function, directly. All should take one argument, 'x', which can be either a numeric vector or numeric scalar. log.transformation.derivative may be supplied as NULL; the other three functions must be defined

name

A character value with a descriptive name of the transformation

The Discrete_Set_Distribution class

Description

A class that represents a discrete probability distribution over an arbitrary set of numbers

Slots

values: The numeric set of values
weights: The probability of each value in the set. Sum to 1

An object representing support over an arbitrary set of real numbers

Description

An object representing support over an arbitrary set of real numbers

Create a distribution representing a Discrete Set

Description

Creates an object representing a discrete probability distribution over an arbitrary set of numbers

Usage

Discrete.Set.Distribution(values, weights, var.name = NULL)
Discrete.Set.Distribution(values, weights, var.name = NULL)

Arguments

values

The numeric set of values

weights

The weight given to the corresponding value. Need not sum to 1

var.name

The name of the single variable in the distribution, or NULL if no name is specified

Create a support over an arbitrary set of values

Description

Create a support over an arbitrary set of values

Usage

Discrete.Set.Support(supported.values)
Discrete.Set.Support(supported.values)

Arguments

supported.values

A numeric vector of the allowed values in this support

Value

An object of class Discrete_Set_Support

The abstract superclass for all Distribution objects

Description

Distribution objects represent a distribution of one or more variables

Slots

var.names: A character vector of the names of the variables in the distribution (optional)
n.var: The number of variables in the distribution
support: A Support object defining the support for each variable in the distribution
is.improper: A logical vectors indicating whether each variable in the distribution is improper

Tests whether two Distribution objects represent the same distribution

Description

Evaluates to true if the two distributions produce the same random samples

Usage

distributions.equal(dist1, dist2)
distributions.equal(dist1, dist2)

Arguments

dist1, dist2

The distributions to compare

Details

The variable order must be the same for two multivariate distributions, otherwise the equality test will return false

Value

True if the two distributions produce the same random samples

Internal function for subclasses to calculate the density for a distribution

Description

This function is provided to be overriden by developers. End users should instead call calculate.density

Usage

do.calculate.density(dist, x, log = F, n.sim = 1000)
do.calculate.density(dist, x, log = F, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

x

A matrix where each row represents one point and each column represents a variable in the distribution (the wrapper matches variable names before passing to this function)

log

A logical indicating whether to return the density on the log scale

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

The wrapper calculate.density takes care of matching variable names and of formatting the return value

Value

If x is a vector, a scalar density. If x is a matrix, a numeric vector of densities, one for each row in x

The Empiric_Distribution Class

Description

A class that defines a distribution based on a set of samples from that distribution. Treats the samples as coming from a discrete distribution. For a continuous representation, see Smoothed_Empiric_Distribution

Slots

points: A matrix containing the samples
weights: A numeric vector with the weight given to each row in points. Sum to 1
n.points: The number of rows in points

Create an empiric distribution from a set of samples

Description

This is a convenience alias for the formal constructor, new('Empiric_Distribution', ...)

Usage

Empiric.Distribution(points, weights = 1, var.names = NULL)
Empiric.Distribution(points, weights = 1, var.names = NULL)

Arguments

points

A matrix of values, where each row represents one sample and each column represents one variable. If a numeric vector is passed, assumed to be samples from a univariate distribution

weights

A numeric vector of weights, one for each row in points

var.names

The names of the variables in the distribution. If NULL, uses the column names from points

Generate marginal random samples for each variable in a distribution

Description

Generates random samples for each variable in the distribution, but does NOT preserve the correlations across variables within samples. For some distribution implementations, this can be substantially faster than generating true, multivariate random samples, so this method is preferred if random samples are only needed for one variable at a time

Usage

generate.random.marginal.samples(dist, n)
generate.random.marginal.samples(dist, n)

Arguments

dist

An object of class Distribution or a subclass

n

The number of random samples to be generated

Details

Note to developers: this function should not be overridden. Override do.generate.random.marginal.samples instead

Value

If n==1, a numeric vector with one value for each variable in the distribution. If there is only one variable in the distribution, a numeric vector with n values. If n>1 and there is more than one variable in the distribution, a matrix with n rows, where each row represents one random sample, and each column represents a variable in the distribution

Generate random samples from a distribution

Description

Generate random samples from a distribution

Usage

generate.random.samples(dist, n)
generate.random.samples(dist, n)

Arguments

dist

An object of class Distribution or a subclass

n

The number of random samples to be generated

Details

Note to developers: This function should not be overridden directly. Insteady override do.generate.random.samples

Value

Get the variance-covariance matrix for variables in a distribution

Description

Get the variance-covariance matrix for variables in a distribution

Usage

get.covariance.matrix(dist, n.sim = 1000)
get.covariance.matrix(dist, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

Note to developers: this function should not be overridden. Override do.get.covariance.matrix instead

Value

A square matrix of dimension number variables in distribution representing the variance-covariance matrix for the distribution

Get Pre-Defined Transformation Objects by Name

Description

Gets a pre-defined transformation object. The available transformations are 'log', 'logit', and 'identity'

Usage

get.defined.transformation(transformation.names, throw.error.if.no.match = F)
get.defined.transformation(transformation.names, throw.error.if.no.match = F)

Value

If transformation.names is a single character value, returns an object of class transformation. Otherwise, returns a list of transformation objects

Get a function that calculates the density for the distribution

Description

A convenience function that packages up a call to calculate.density on this distribution into its own stand-alone function (which could be passed along as an argument to other functions)

Usage

get.density.function(dist, default.log = T, n.sim = 1000)
get.density.function(dist, default.log = T, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

default.log

Whether the returned function should calculate the density on the log scale (by default, the returned function can have a log parameter set explicitly)

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Value

A function that takes two arguments. The first, mandatory, is 'x' - the values of the parameters at which to calculate the density. May be either a vector, if the density at a single point is desired, or a matrix where each row represents one point and each column represents a variable in the distribution The second, optional, is 'log' - whether to calculate the density on the log scale. By default, log is set to default.log

Get the description of a Distribution object

Description

Get the description of a Distribution object

Usage

get.description(object)
get.description(object)

Arguments

object

The object to describe

Get equal-tailed intervals (confidence/credible intervals) for the variables in a distribution

Description

Get equal-tailed intervals (confidence/credible intervals) for the variables in a distribution

Usage

get.equal.tailed.intervals(dist, coverage = 0.95, n.sim = 1000)
get.equal.tailed.intervals(dist, coverage = 0.95, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

coverage

A vector of probabilities (from 0 to 1) which the intervals should cover

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

Note to developers: This function should not be overridden directly. Insteady override do.get.equal.tailed.intervals

Value

If length(coverage)==1, and the distribution has one variable, returns a numeric vector with two values: the lower and upper bound of the interval. If length(coverage)==1 and the distribution has more than one variable, returns a matrix with one row for the lower bound and one row for the upper, and one column for each variable. If length(coverage)>1 and the distribution has one variable, returns a matrix with one row for the lower bound and one row for the upper bound, and one column for each value in coverage. If length(coverage)>1, and the distribution has more than one variable returns a 3-dimensional array; the first dimension has values 'lower' and 'upper'. The second dimension has one value for each variable. The third dimension has one value for each value of coverage.

Get highest-density intervals (confidence/credible intervals) for the variables in a distribution

Description

Get highest-density intervals (confidence/credible intervals) for the variables in a distribution

Usage

get.highest.density.intervals(dist, coverage = 0.95, n.sim = 1000)
get.highest.density.intervals(dist, coverage = 0.95, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

coverage

A vector of probabilities (from 0 to 1) which the intervals should cover

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

Note to developers: This function should not be overridden directly. Insteady override do.get.highest.density.intervals

Value

Get intervals (confidence/credible intervals) for the variables in a distribution

Description

Get intervals (confidence/credible intervals) for the variables in a distribution

Usage

get.intervals(
  dist,
  type = c("equal-tailed", "highest-density")[1],
  coverage = 0.95,
  n.sim = 1000
)
get.intervals(
  dist,
  type = c("equal-tailed", "highest-density")[1],
  coverage = 0.95,
  n.sim = 1000
)

Arguments

dist

An object of class Distribution or a subclass

type

Either 'equal-tailed' or 'highest-density' depending on the type of interval desired (equal-tailed is generally easier to compute)

coverage

A vector of probabilities (from 0 to 1) which the intervals should cover

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

Note to developers: this function should not be overridden. Override do.get.equal.tailed.intervals and do.get.highest.density.intervals instead

Value

Get means of the variables in a distribution

Description

Get means of the variables in a distribution

Usage

get.means(dist, n.sim = 1000)
get.means(dist, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

Note to developers: this function should not be overridden. Override do.get.means instead

Value

A numeric vector with a mean for each variable in the distribution

Get medians of the variables in a distribution

Description

Get medians of the variables in a distribution

Usage

get.medians(dist, n.sim = 1000)
get.medians(dist, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

Note to developers: This function should not be overridden directly. Insteady override do.get.medians

Value

A numeric vector with a median for each variable in the distribution

Get quantiles for the variables in a distribution

Description

Get quantiles for the variables in a distribution

Usage

get.quantiles(dist, p, lower.tail = T, log.p = F, n.sim = 1000)
get.quantiles(dist, p, lower.tail = T, log.p = F, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

p

A vector of probabilities for which to get the quantiles

lower.tail

If true, the returned values are the greatest values x for each variable such that $P(X \leq x) \geq p$ . If fale, the returned values are the smallest values x for each variable such that $P(X > x) \geq p$ . This can be either a scalar (in which case the value is applied to all quantiles), or a vector with one logical value for each value of p

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

Note to developers: This function should not be overridden directly. Insteady override do.get.quantiles

Value

If there is only one variable in the distribution, a vector of quantiles for each value of p. If p is length one, a vector of quantiles for each variable in the distribution. If there is more than one variable in the distribution and p>1, a matrix with one row for each value of p, where each column represents a variable in the distribution

Get a function that generates random samples form the distribution

Description

A convenience function that packages up a call to generate.random.samples on this distribution into its own stand-alone function (which could be passed along as an argument to other functions)

Usage

get.random.generator.function(dist)
get.random.generator.function(dist)

Arguments

dist

An object of class Distribution or a subclass

Value

A function that takes one argument, 'n' - the number of random samples to generate

Get the standard deviations of the variables in a distribution

Description

Get the standard deviations of the variables in a distribution

Usage

get.sds(dist, n.sim = 1000)
get.sds(dist, n.sim = 1000)

Arguments

dist

An object of class Distribution or a subclass

n.sim

If the values are to be calculated by random sample generation, how many random samples to generate

Details

Note to developers: this function should not be overridden. Override do.get.sds instead

Value

A numeric vector with a standard deviation for each variable in the distribution

Get the maximum and minimm values within a support over real numbers

Description

Get the maximum and minimm values within a support over real numbers

Usage

get.support.bounds(support)
get.support.bounds(support)

Arguments

support

An object of class Support

Value

If called on an object of class Support, returns a numeric vector of length 2, with lower and upper bounds. If called on a list containing only Support objects, returns a matrix with two rows (lower and upper bounds) and a column for each element in the list

Create an object which represents support over a range of integers

Description

Create an object which represents support over a range of integers

Usage

Integer.Support(lower, upper, lower.inclusive = T, upper.inclusive = T)
Integer.Support(lower, upper, lower.inclusive = T, upper.inclusive = T)

Arguments

lower

upper

lower.inclusive

upper.inclusive

Value

An object of class Range_Support, such that is.supported is true if x falls within any of the ranges lower[i] to upper[i]

Test if numeric values fall within a defined support

Description

Test if numeric values fall within a defined support

Usage

is.supported(support, x, by.variable = F)
is.supported(support, x, by.variable = F)

Arguments

support

An object of class Support

x

If the support is univariate, a numeric vector. If the support is multivariate, a matrix with one column for each variable and one row for each point to test or a numeric vector with one value for each variable in the support

by.variable

If this is a Multivariate_Support, if by.variable is TRUE, calculates support for each variable independently

Value

If the support is univariate or if by.variable==FALSE or if only a vector is passed to x, returns a logical vector, with one value for each value of x, corresponding to whether that value of x falls within the defined support. If the support is multivariate and by.variable==TRUE and a matrix with more than one row was passed to x, returns a matrix with one column for each variable and one row for each point

Join Multiple Distributions

Description

Joins multiple Distribution objects into a single Distribution object, on the premise that the variables in each sub-distribution are independent of the variables in any other sub-distribution

Usage

join.distributions(..., var.names = NULL)
join.distributions(..., var.names = NULL)

Arguments

...

One or more Distribution objects or lists of Distribution objects to be joined. If var.names are set on the component distributions, those names will be preserved. If not, and if the elements of ... are named (or elements in lists contained in ... are named), those names will be used as the var.names for the corresponding sub-distributions

Value

An object of class Joint_Independent_Distributions

The Joint_Independent_Distributions class

Description

A class that joins multiple independent sub-distributions into a joint distribution

Slots

subdistributions: A list of the Distribution objects representing the component distributions of this joint distribution
indices.for.subdistributions: A list whose elements are integer vectors, such that indices.for.subdistributions[[i]] is the indices into the overall distribution of the variables represented by subdistributions[[i]]
n.subdistributions: The number of component distributions

Create a Univariate Logit-Normal Distribution Object

Description

Create a Univariate Logit-Normal Distribution Object

Usage

Logitnormal.Distribution(
  meanlogit,
  sdlogit,
  lower = 0,
  upper = 1,
  var.name = NULL
)
Logitnormal.Distribution(
  meanlogit,
  sdlogit,
  lower = 0,
  upper = 1,
  var.name = NULL
)

Arguments

meanlogit, sdlogit

The mean and standard deviation (on the logit scale) of the distribution

lower, upper

The lower and the upper bounds (on the original scale, NOT the logit scale), if this is a bounded distribution

var.name

The name of the single variable in the distribution, or NULL if no name is specified

Create a Mixture Univariate Logit-Normal Distributions

Description

Create a Mixture Univariate Logit-Normal Distributions

Usage

Logitnormal.Mixture(
  meanslogit,
  sdslogit,
  weights = 1,
  lower = 0,
  upper = 1,
  var.name = NULL
)
Logitnormal.Mixture(
  meanslogit,
  sdslogit,
  weights = 1,
  lower = 0,
  upper = 1,
  var.name = NULL
)

Arguments

meanslogit, sdslogit

The means and standard deviations (on the logit scale) of the components of the distribution

weights

The weights applied to each component of the mixture. Weights need not be normalized to sum to 1. If a scalar value is given, all components of the mixture will have the same weight

lower, upper

The lower and the upper bounds (on the original scale, NOT the logit scale), if this is a bounded distribution (the same bounds apply for all components of the mixture)

Create a Logit-Uniform Distribution Object

Description

Create a Logit-Uniform Distribution Object

Usage

Logituniform.Distribution(min = 0, max = 1, var.name = NULL)
Logituniform.Distribution(min = 0, max = 1, var.name = NULL)

Arguments

min, max

The bounds of the distribution (on the original scale, NOT the logit scale). If min is 0 or max is 1, returns an improper logit-uniform distribution (which returns 1/x/(1-x) for all densities, but cannot evaluate cdfs, quantiles, or generate random samples)

var.name

The name of the single variable in the distribution, or NULL if no name is specified

Create a Univariate Log-Normal Distribution Object

Description

Create a Univariate Log-Normal Distribution Object

Usage

Lognormal.Distribution(
  meanlog = 0,
  sdlog = 1,
  lower = 0,
  upper = Inf,
  var.name = NULL
)
Lognormal.Distribution(
  meanlog = 0,
  sdlog = 1,
  lower = 0,
  upper = Inf,
  var.name = NULL
)

Arguments

meanlog, sdlog

The mean and standard deviation (on the log scale) of the distribution

lower, upper

The lower and the upper bounds (on the original scale, NOT the log scale), if this is a bounded distribution

var.name

The name of the single variable in the distribution, or NULL if no name is specified

Create a Mixture of Univariate Log-Normal Distributions

Description

Create a Mixture of Univariate Log-Normal Distributions

Usage

Lognormal.Mixture(
  meanslog = 0,
  sdslog = 1,
  weights = 1,
  lower = 0,
  upper = Inf,
  var.name = NULL
)
Lognormal.Mixture(
  meanslog = 0,
  sdslog = 1,
  weights = 1,
  lower = 0,
  upper = Inf,
  var.name = NULL
)

Arguments

meanslog, sdslog

The means and standard deviations (on the log scale) of the components of distribution

weights

The weights applied to each component of the mixture. Weights need not be normalized to sum to 1. If a scalar value is given, all components of the mixture will have the same weight

lower, upper

The lower and the upper bounds (on the original scale, NOT the log scale), if this is a bounded distribution (the same bounds apply for all components of the mixture)

Create a Log-Uniform Distribution Object

Description

Create a Log-Uniform Distribution Object

Usage

Loguniform.Distribution(min = 0, max = 1, var.name = NULL)
Loguniform.Distribution(min = 0, max = 1, var.name = NULL)

Arguments

min, max

The bounds of the distribution (on the original scale, NOT the log scale). If min is 0 or max is Inf, returns an improper log-uniform distribution (which returns 1/x for all densities, but cannot evaluate cdfs, quantiles, or generate random samples)

var.name

The name of the single variable in the distribution, or NULL if no name is specified

The Multivariate_Normal_Distribution Class

Description

Defines a multivariate normal distribution

Slots

mu,sigma: The mean vector and covariance matrix of the distribution

An object representing support (on the real numbers) over across multiple variables

Description

An object representing support (on the real numbers) over across multiple variables

Create a Multivariate Uniform Distribution Object Where the Variables are Correlated

Description

Uses a rough approximation to generate a multivariate normal distribution such that the correlations between variables are approximately equal to the given correlation.matrix. Specifically, generates random samples from a multivariate normal distribution with mean=0 and covariance matrix = cov2cor(correlation.matrix + 0.04*I)

Usage

Multivariate.Correlated.Uniform.Distribution(
  correlation.matrix,
  min = rep(0, dim(correlation.matrix)[1]),
  max = rep(1, dim(correlation.matrix)[1]),
  var.names = NULL
)
Multivariate.Correlated.Uniform.Distribution(
  correlation.matrix,
  min = rep(0, dim(correlation.matrix)[1]),
  max = rep(1, dim(correlation.matrix)[1]),
  var.names = NULL
)

Arguments

correlation.matrix

The matrix specifying how variables should be correlated

min, max

The vectors of minima and maxima for each variable in the distribution. If given a scalar value, assumes that value applies for all variables

var.names

The names of the variables in the distribution. If NULL, uses the names of mu, the row names of sigma, or the column names of sigma, in that order

Create a Multivariate Logit-Normal Distribution Object

Description

Create a Multivariate Logit-Normal Distribution Object

Usage

Multivariate.Logitnormal.Distribution(
  mu = rep(0, nrow(sigma)),
  sigma = diag(rep(1, length(mu))),
  lower = 0,
  upper = Inf,
  var.names = NULL
)
Multivariate.Logitnormal.Distribution(
  mu = rep(0, nrow(sigma)),
  sigma = diag(rep(1, length(mu))),
  lower = 0,
  upper = Inf,
  var.names = NULL
)

Arguments

mu, sigma

The mean vector and covariance matrix of the distribution (after logit transformation)

lower, upper

The upper and lower bounds for each variable (on the original scale, NOT the logit scale). If only one value is given, assumed to apply to all variables in the distribution

var.names

The names of the variables in the distribution. If NULL, uses the names of mu, the row names of sigma, or the column names of sigma, in that order

Create a Multivariate Log-Normal Distribution Object

Description

Create a Multivariate Log-Normal Distribution Object

Usage

Multivariate.Lognormal.Distribution(
  mu = rep(0, nrow(sigma)),
  sigma = diag(rep(1, length(mu))),
  lower = 0,
  upper = Inf,
  var.names = NULL
)
Multivariate.Lognormal.Distribution(
  mu = rep(0, nrow(sigma)),
  sigma = diag(rep(1, length(mu))),
  lower = 0,
  upper = Inf,
  var.names = NULL
)

Arguments

mu, sigma

The mean vector and covariance matrix of the distribution (after log transformation)

lower, upper

The upper and lower bounds for each variable (on the original scale, NOT the log scale). If only one value is given, assumed to apply to all variables in the distribution

var.names

The names of the variables in the distribution. If NULL, uses the names of mu, the row names of sigma, or the column names of sigma, in that order

Create a Multivariate Normal Distribution Object

Description

Create a Multivariate Normal Distribution Object

Usage

Multivariate.Normal.Distribution(
  mu = rep(0, nrow(sigma)),
  sigma = diag(rep(1, length(mu))),
  lower = -Inf,
  upper = Inf,
  var.names = NULL
)
Multivariate.Normal.Distribution(
  mu = rep(0, nrow(sigma)),
  sigma = diag(rep(1, length(mu))),
  lower = -Inf,
  upper = Inf,
  var.names = NULL
)

Arguments

mu, sigma

The mean vector and covariance matrix of the distribution

lower, upper

The upper and lower bounds for each variable, if bounded. If only one value is given, assumed to apply to all variables in the distribution

var.names

The names of the variables in the distribution. If NULL, uses the names of mu, the row names of sigma, or the column names of sigma, in that order

Join multiple Support objects into a multivariate Support

Description

Join multiple Support objects into a multivariate Support

Usage

Multivariate.Support(...)
Multivariate.Support(...)

Arguments

...

Objects of class Support, or lists that contain only objects of class Support

Value

A Multivariate_Support object

Create a Univariate Normal Distribution Object

Description

Create a Univariate Normal Distribution Object

Usage

Normal.Distribution(
  mean = 0,
  sd = 1,
  lower = -Inf,
  upper = Inf,
  var.name = NULL
)
Normal.Distribution(
  mean = 0,
  sd = 1,
  lower = -Inf,
  upper = Inf,
  var.name = NULL
)

Arguments

mean, sd

The mean and standard deviation of the distribution

lower, upper

The lower and the upper bounds, if this is a bounded distribution

var.name

The name of the single variable in the distribution, or NULL if no name is specified

Create a Mixture of Univariate Normal Distributions

Description

Create a Mixture of Univariate Normal Distributions

Usage

Normal.Mixture(
  means = 0,
  sds = 1,
  weights = 1,
  lower = -Inf,
  upper = Inf,
  var.name = NULL
)
Normal.Mixture(
  means = 0,
  sds = 1,
  weights = 1,
  lower = -Inf,
  upper = Inf,
  var.name = NULL
)

Arguments

means, sds

The means and standard deviations of each component of the mixture

weights

The weights applied to each component of the mixture. Weights need not be normalized to sum to 1. If a scalar value is given, all components of the mixture will have the same weight

lower, upper

The lower and the upper bounds, if this is a bounded distribution (the same bounds apply for all components of the mixture)

An object representing support over a range of real numbers

Description

An object representing support over a range of real numbers

Separate a distribution object into a list of distributions that are independent from each other

Description

Separate a distribution object into a list of distributions that are independent from each other

Usage

separate.independent.distributions(object, var.names)
separate.independent.distributions(object, var.names)

Arguments

object

A distribution object

Value

A list of Distribution objects, where each distribution either (a) is univariate or (b) contains only correlated variables

Sets the variable names for a Distribution Object

Description

Sets the variable names for a Distribution Object

Usage

set.var.names(object, var.names)
set.var.names(object, var.names)

Arguments

var.names

The character vector of variable names

Value

A Distribution object with the new var.names set

The Smoothed_Empiric_Distribution Class

Description

A class that defines a distribution based on a set of samples from that distribution, but applies Gaussian kernel smoothers. For an unsmoothed representation, see Empiric_Distribution

Slots

points: A matrix containing the samples
weights: A numeric vector with the weight given to each row in points. Sum to 1
n.points: The number of rows in points

Create an smoothed empiric distribution from a set of samples

Description

Create an smoothed empiric distribution from a set of samples

Usage

Smoothed.Empiric.Distribution(
  points,
  weights = 1,
  var.names = NULL,
  bandwidth.multipliers = 1
)
Smoothed.Empiric.Distribution(
  points,
  weights = 1,
  var.names = NULL,
  bandwidth.multipliers = 1
)

Arguments

points

A matrix of values, where each row represents one sample and each column represents one variable. If a numeric vector is passed, assumed to be samples from a univariate distribution

weights

A numeric vector of weights, one for each row in points

var.names

The names of the variables in the distribution. If NULL, uses the column names from points

Get a distribution that describes a subset of the variables in a given distribution

Description

Get a distribution that describes a subset of the variables in a given distribution

Usage

subset.distribution(dist, vars.to.keep)
subset.distribution(dist, vars.to.keep)

Arguments

dist

An object of class Distribution or a subclass

vars.to.keep

Either a character vector with the names of the variables to keep, an integer/numeric vector with the indices of the variables to keep, or a logical vector of length n.var indicating which variables to keep

Details

Note to developers: this function should not be overridden. Override do.subset.distribution instead

Value

An object of class Distribution-class

Subset a Support object

Description

Subset a Support object

Usage

subset.support(support, keep)
subset.support(support, keep)

Arguments

support

An object of class Support

keep

Which dimensions of the support to keep. Either a set of integer indices or a logical vector

Value

A Support object

An object representing support over real numbers

Description

An object representing support over real numbers

Join multiple univariate Support objects into one univariate Support

Description

Join multiple univariate Support objects into one univariate Support

Usage

Support.Union(...)
Support.Union(...)

Arguments

...

Objects of class Support, or lists that contain only objects of class Support

Value

A Union_Support object, such that is.supported is true if is.supported is true for any of its component supports

The transformation class

Description

A class that represents a functional transformation, along with how to reverse the transformation and take its derivative

Slots

transform.function,reverse.transform.function,transformation.derivative,log.abs.transformation.derivative: Functions that compute the transformation, inverse transformation, derivative of the transformation function, and log of the absolute value of the derivative of the transformation function, directly. All should take one argument, 'x', which can be either a numeric vector or numeric scalar. log.abs.transformation.derivative may be supplied as NULL; the other three functions must be defined
name: A character value with a descriptive name of the transformation

Create a transformed multivariate normal distribution object

Description

Creates a distribution where all the variables, after arbitrary transformations, follow a normal distribution

Usage

Transformed.Multivariate.Normal.Distribution(
  mu = rep(0, nrow(sigma)),
  sigma = diag(rep(1, length(mu))),
  lower = -Inf,
  upper = Inf,
  var.names = NULL,
  transformations = NULL
)
Transformed.Multivariate.Normal.Distribution(
  mu = rep(0, nrow(sigma)),
  sigma = diag(rep(1, length(mu))),
  lower = -Inf,
  upper = Inf,
  var.names = NULL,
  transformations = NULL
)

Arguments

mu, sigma

The mean vector and covariance matrix of the distribution (after transformations)

lower, upper

The upper and lower bounds for each variable (on the original scale, NOT the transformed scale). If only one value is given, assumed to apply to all variables in the distribution

var.names

The names of the variables in the distribution. If NULL, uses the names of mu, the row names of sigma, or the column names of sigma, in that order

transformations

Create a Distribution of a Random Variable that is Normal after an arbitrary transformation

Description

Create a Distribution of a Random Variable that is Normal after an arbitrary transformation

Usage

Transformed.Normal.Distribution(
  mean = 0,
  sd = 1,
  transformation = NULL,
  lower = -Inf,
  upper = Inf,
  var.name = NULL
)
Transformed.Normal.Distribution(
  mean = 0,
  sd = 1,
  transformation = NULL,
  lower = -Inf,
  upper = Inf,
  var.name = NULL
)

Arguments

mean, sd

The mean and standard deviation of the random variable (after transformation has been applied)

lower, upper

The lower and the upper bounds, if this is a bounded distribution. The bounds are on the ORIGINAL scale (before transformation).

var.name

The name of the single variable in the distribution, or NULL if no name is specified

Create a Mixture of Transformed Normal Distributions

Description

Creates a mixture of distributions representing random variables that are normal after transformation (eg, mixture of normals, log-normals, logit-normals, etc.)

Usage

Transformed.Normal.Mixture(
  means = 0,
  sds = 1,
  weights = 1,
  transformation = NULL,
  lower = -Inf,
  upper = Inf,
  var.name = NULL
)
Transformed.Normal.Mixture(
  means = 0,
  sds = 1,
  weights = 1,
  transformation = NULL,
  lower = -Inf,
  upper = Inf,
  var.name = NULL
)

Arguments

means, sds

The means and standard deviations of each component of the mixture (after transformation has been applied)

weights

The weights applied to each component of the mixture. Weights need not be normalized to sum to 1. If a scalar value is given, all components of the mixture will have the same weight

lower, upper

The lower and the upper bounds, if this is a bounded distribution. The bounds are on the ORIGINAL scale (before transformation). The same bounds apply for all components of the mixture

Create a Uniform Distribution Object

Description

Create a Uniform Distribution Object

Usage

Uniform.Distribution(min = 0, max = 1, var.name = NULL)
Uniform.Distribution(min = 0, max = 1, var.name = NULL)

Arguments

min, max

The bounds of the distribution. If either is infinite, will create an improper uniform distribution (which returns 1 for all densities, but cannot evaluate cdfs, quantiles, or generate random samples)

var.name

The name of the single variable in the distribution, or NULL if no name is specified

An object representing the union of two or more supports over a range of real numbers

Description

An object representing the union of two or more supports over a range of real numbers

The Univariate_Canonical_Distribution class

Description

A class that represents a univariate canonical distribution, such as a normal or beta distribution

Slots

name: A short, descriptive name for the distribution
density.function.name,cdf.function.name,quantile.function.name: Names of the (elsewhere defined) functions that calculate density, cdf, and quantiles (eg 'dnorm', 'pnorm', and 'qnorm)
parameters: A list of parameters that would be passed to density.function, cdf.function, and quantile.function. For example, for a normal(0,1), parameters=list(mean=0, sd=1)
p.in.bounds,log.p.in.bounds: The cumulative probability and of the log cumulative probability between the lower and upper bounds
p.lower.bound: The value of the cdf evaluated at the lower bound
transformation: An object of class transformation, defining the transformation applied to the variable before applying the distribution (eg, )
mean.value,variance: If known, the mean and variance of the distribution. May be NA

Create a distribution object based off of a canonical, univariate distribution

Usage

Univariate.Canonical.Distribution(
  name,
  dist.name,
  parameters,
  var.name = NULL,
  support = Continuous.Support(),
  density.function.name = paste0("d", dist.name),
  cdf.function.name = paste0("p", dist.name),
  quantile.function.name = paste0("q", dist.name),
  transformation = NULL,
  is.improper = F,
  mean.value = as.numeric(NA),
  variance.value = as.numeric(NA)
)
Univariate.Canonical.Distribution(
  name,
  dist.name,
  parameters,
  var.name = NULL,
  support = Continuous.Support(),
  density.function.name = paste0("d", dist.name),
  cdf.function.name = paste0("p", dist.name),
  quantile.function.name = paste0("q", dist.name),
  transformation = NULL,
  is.improper = F,
  mean.value = as.numeric(NA),
  variance.value = as.numeric(NA)
)

Arguments

name

A short, descriptive name for the distribution

dist.name

parameters

A list of parameters that would be passed to d/r/p functions in R. For example, for a normal(0,1), parameters=list(mean=0, sd=1)

var.name

The name of the variable in this distribution

support

A support object that

transformation

is.improper

Logicals indicating whether the distribution is improper/discrete

mean.value, variance

If known, these values will be returned for calls to get.means, get.sds, get.covariance.matrix. If passed NA, random sampling will be used to estimate distribution parameters if requested

density.function, cdf.function, quantile.function

Package 'distributions'

Help Index

Create a multivariate normal distribution with a Continuous Autoregressive 1 (CAR-1) correlation structure

Description

Usage

Arguments

See Also

Create a Univariate Bernoulli Distribution Object

Description

Usage

Arguments

See Also

Create a Univariate Beta Distribution Object

Description

Usage

Arguments

See Also

Create a Univariate Binomial Distribution Object

Description

Usage

Arguments

See Also

Calculate the cumulative distribution function for a distribution

Description

Usage

Arguments

Details

Value

Calculate a marginal cumulative distribution function for each variable in a distribution

Description

Usage

Arguments

Details

Value

Calculate a marginal density for each variable in a distribution

Description

Usage

Arguments

Details

Value

The Canonical_Mixture_Distribution class

Description

Slots

See Also

Create a mixture distribution object based off of a canonical, univariate distribution

Usage

Arguments

See Also

Create a multivariate normal distribution with a Compound Symmetry correlation structure

Description

Usage

Arguments

See Also

The Constant_Distribution class

Description

Slots

See Also

Create a distribution representing a Constant Distribution

Description

Usage

Arguments

See Also

Create an object which represents support over a range of integers

Description

Usage

Arguments

Value

Create an object representing a transformation

Description

Usage

Arguments

The Discrete_Set_Distribution class

Description

Slots

See Also

An object representing support over an arbitrary set of real numbers

Description

Create a distribution representing a Discrete Set

Description

Usage