MultivariateNormal: Multivariate Normal Distribution Class
In RaphaelS1/distr6: The Complete R6 Probability Distributions Interface
MultivariateNormal R Documentation
Multivariate Normal Distribution Class
Description
Mathematical and statistical functions for the Multivariate Normal distribution, which
is commonly used to generalise the Normal distribution to higher dimensions, and is commonly associated with Gaussian Processes.
Details
The Multivariate Normal distribution parameterised with mean, \mu, and covariance matrix, \Sigma, is defined by the pdf,
f(x_1,...,x_k) = (2 * \pi)^{-k/2}det(\Sigma)^{-1/2}exp(-1/2(x-\mu)^T\Sigma^{-1}(x-\mu))
for \mu \epsilon R^{k} and \Sigma \epsilon R^{k x k}.
Sampling is performed via the Cholesky decomposition using chol.
Number of variables cannot be changed after construction.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on the Reals and only when the covariance matrix is positive-definite.
Default Parameterisation
MultiNorm(mean = rep(0, 2), cov = c(1, 0, 0, 1))
Omitted Methods
cdf and quantile
are
omitted as no closed form analytic expression could be found, decorate with FunctionImputation for a numerical imputation.
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> MultivariateNormal
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
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Inherited methods
distr6::Distribution$cdf()distr6::Distribution$confidence()distr6::Distribution$correlation()distr6::Distribution$iqr()distr6::Distribution$liesInSupport()distr6::Distribution$liesInType()distr6::Distribution$median()distr6::Distribution$parameters()distr6::Distribution$pdf()distr6::Distribution$prec()distr6::Distribution$print()distr6::Distribution$quantile()distr6::Distribution$rand()distr6::Distribution$stdev()distr6::Distribution$strprint()distr6::Distribution$summary()distr6::Distribution$workingSupport()
Method new()
Creates a new instance of this R6 class.
Number of variables cannot be changed after construction.
Usage
MultivariateNormal$new(
mean = rep(0, 2),
cov = c(1, 0, 0, 1),
prec = NULL,
decorators = NULL
)
Arguments
mean(numeric())
Vector of means, defined on the Reals.
cov(matrix()|vector())
Covariance of the distribution, either given as a matrix or vector coerced to a
matrix via matrix(cov, nrow = K, byrow = FALSE). Must be semi-definite.
prec(matrix()|vector())
Precision of the distribution, inverse of the covariance matrix. If supplied then cov is
ignored. Given as a matrix or vector coerced to a
matrix via matrix(cov, nrow = K, byrow = FALSE). Must be semi-definite.
decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = \sum p_X(x)*x
with an integration analogue for continuous distributions.
Usage
MultivariateNormal$mean(...)
Arguments
...Unused.
Method mode()
The mode of a probability distribution is the point at which the pdf is
a local maximum, a distribution can be unimodal (one maximum) or multimodal (several
maxima).
Usage
MultivariateNormal$mode(which = "all")
Arguments
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies
which mode to return.
Method variance()
The variance of a distribution is defined by the formula
var_X = E[X^2] - E[X]^2
where E_X is the expectation of distribution X. If the distribution is multivariate the
covariance matrix is returned.
Usage
MultivariateNormal$variance(...)
Arguments
...Unused.
Method entropy()
The entropy of a (discrete) distribution is defined by
- \sum (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for
continuous distributions.
Usage
MultivariateNormal$entropy(base = 2, ...)
Arguments
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)
...Unused.
Method mgf()
The moment generating function is defined by
mgf_X(t) = E_X[exp(xt)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
MultivariateNormal$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...Unused.
Method cf()
The characteristic function is defined by
cf_X(t) = E_X[exp(xti)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
MultivariateNormal$cf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...Unused.
Method pgf()
The probability generating function is defined by
pgf_X(z) = E_X[exp(z^x)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
MultivariateNormal$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
Method getParameterValue()
Returns the value of the supplied parameter.
Usage
MultivariateNormal$getParameterValue(id, error = "warn")
Arguments
idcharacter()
id of parameter support to return.
error(character(1))
If "warn" then returns a warning on error, otherwise breaks if "stop".
Method setParameterValue()
Sets the value(s) of the given parameter(s).
Usage
MultivariateNormal$setParameterValue(
...,
lst = list(...),
error = "warn",
resolveConflicts = FALSE
)
Arguments
...ANY
Named arguments of parameters to set values for. See examples.
lst(list(1))
Alternative argument for passing parameters. List names should be parameter names and list values
are the new values to set.
error(character(1))
If "warn" then returns a warning on error, otherwise breaks if "stop".
resolveConflicts(logical(1))
If FALSE (default) throws error if conflicting parameterisations are provided, otherwise
automatically resolves them by removing all conflicting parameters.
Method clone()
The objects of this class are cloneable with this method.
Usage
MultivariateNormal$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
References
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01).
Michael P. McLaughlin.
Gentle, J.E. (2009).
Computational Statistics.
Statistics and Computing. New York: Springer. pp. 315–316.
doi:10.1007/978-0-387-98144-4. ISBN 978-0-387-98143-7.
See Also
Other continuous distributions:
Arcsine,
BetaNoncentral,
Beta,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Dirichlet,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Gompertz,
Gumbel,
InverseGamma,
Laplace,
Logistic,
Loglogistic,
Lognormal,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
Other multivariate distributions:
Dirichlet,
EmpiricalMV,
Multinomial
RaphaelS1/distr6 documentation built on Feb. 24, 2024, 9:14 p.m.
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| MultivariateNormal | R Documentation |
Multivariate Normal Distribution Class
Description
Mathematical and statistical functions for the Multivariate Normal distribution, which is commonly used to generalise the Normal distribution to higher dimensions, and is commonly associated with Gaussian Processes.
Details
The Multivariate Normal distribution parameterised with mean, \mu, and covariance matrix, \Sigma, is defined by the pdf,
f(x_1,...,x_k) = (2 * \pi)^{-k/2}det(\Sigma)^{-1/2}exp(-1/2(x-\mu)^T\Sigma^{-1}(x-\mu))
for \mu \epsilon R^{k} and \Sigma \epsilon R^{k x k}.
Sampling is performed via the Cholesky decomposition using chol.
Number of variables cannot be changed after construction.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on the Reals and only when the covariance matrix is positive-definite.
Default Parameterisation
MultiNorm(mean = rep(0, 2), cov = c(1, 0, 0, 1))
Omitted Methods
cdf and quantile
are
omitted as no closed form analytic expression could be found, decorate with FunctionImputation for a numerical imputation.
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> MultivariateNormal
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
Inherited methods
distr6::Distribution$cdf()distr6::Distribution$confidence()distr6::Distribution$correlation()distr6::Distribution$iqr()distr6::Distribution$liesInSupport()distr6::Distribution$liesInType()distr6::Distribution$median()distr6::Distribution$parameters()distr6::Distribution$pdf()distr6::Distribution$prec()distr6::Distribution$print()distr6::Distribution$quantile()distr6::Distribution$rand()distr6::Distribution$stdev()distr6::Distribution$strprint()distr6::Distribution$summary()distr6::Distribution$workingSupport()
Method new()
Creates a new instance of this R6 class. Number of variables cannot be changed after construction.
Usage
MultivariateNormal$new( mean = rep(0, 2), cov = c(1, 0, 0, 1), prec = NULL, decorators = NULL )
Arguments
mean(numeric())
Vector of means, defined on the Reals.cov(matrix()|vector())
Covariance of the distribution, either given as a matrix or vector coerced to a matrix viamatrix(cov, nrow = K, byrow = FALSE). Must be semi-definite.prec(matrix()|vector())
Precision of the distribution, inverse of the covariance matrix. If supplied thencovis ignored. Given as a matrix or vector coerced to a matrix viamatrix(cov, nrow = K, byrow = FALSE). Must be semi-definite.decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = \sum p_X(x)*x
with an integration analogue for continuous distributions.
Usage
MultivariateNormal$mean(...)
Arguments
...Unused.
Method mode()
The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
Usage
MultivariateNormal$mode(which = "all")
Arguments
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise"all"returns all modes, otherwise specifies which mode to return.
Method variance()
The variance of a distribution is defined by the formula
var_X = E[X^2] - E[X]^2
where E_X is the expectation of distribution X. If the distribution is multivariate the
covariance matrix is returned.
Usage
MultivariateNormal$variance(...)
Arguments
...Unused.
Method entropy()
The entropy of a (discrete) distribution is defined by
- \sum (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for
continuous distributions.
Usage
MultivariateNormal$entropy(base = 2, ...)
Arguments
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)...Unused.
Method mgf()
The moment generating function is defined by
mgf_X(t) = E_X[exp(xt)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
MultivariateNormal$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....Unused.
Method cf()
The characteristic function is defined by
cf_X(t) = E_X[exp(xti)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
MultivariateNormal$cf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....Unused.
Method pgf()
The probability generating function is defined by
pgf_X(z) = E_X[exp(z^x)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
MultivariateNormal$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at....Unused.
Method getParameterValue()
Returns the value of the supplied parameter.
Usage
MultivariateNormal$getParameterValue(id, error = "warn")
Arguments
idcharacter()
id of parameter support to return.error(character(1))
If"warn"then returns a warning on error, otherwise breaks if"stop".
Method setParameterValue()
Sets the value(s) of the given parameter(s).
Usage
MultivariateNormal$setParameterValue( ..., lst = list(...), error = "warn", resolveConflicts = FALSE )
Arguments
...ANY
Named arguments of parameters to set values for. See examples.lst(list(1))
Alternative argument for passing parameters. List names should be parameter names and list values are the new values to set.error(character(1))
If"warn"then returns a warning on error, otherwise breaks if"stop".resolveConflicts(logical(1))
IfFALSE(default) throws error if conflicting parameterisations are provided, otherwise automatically resolves them by removing all conflicting parameters.
Method clone()
The objects of this class are cloneable with this method.
Usage
MultivariateNormal$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
References
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
Gentle, J.E. (2009). Computational Statistics. Statistics and Computing. New York: Springer. pp. 315–316. doi:10.1007/978-0-387-98144-4. ISBN 978-0-387-98143-7.
See Also
Other continuous distributions:
Arcsine,
BetaNoncentral,
Beta,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Dirichlet,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Gompertz,
Gumbel,
InverseGamma,
Laplace,
Logistic,
Loglogistic,
Lognormal,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
Other multivariate distributions:
Dirichlet,
EmpiricalMV,
Multinomial
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