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.

## Value

Returns an R6 object inheriting from class SDistribution.

## 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.

## 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.

N/A

## 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.

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

## Super classes

distr6::Distribution -> distr6::SDistribution -> MultivariateNormal

## Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

alias

Alias of the distribution.

## Active bindings

properties

Returns distribution properties, including skewness type and symmetry.

## Methods

Inherited methods

### Method new()

Creates a new instance of this R6 class. Number of variables cannot be changed after construction.

#### 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).

#### 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.

#### 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.

#### Arguments

z

(integer(1))
z integer to evaluate probability generating function at.

...

Unused.

### Method getParameterValue()

Returns the value of the supplied parameter.

MultivariateNormal$getParameterValue(id, error = "warn") #### Arguments id character() id of parameter support to return. error (character(1)) If "warn" then returns a warning on error, otherwise breaks if "stop". ### Method setParameterValue() Sets the value(s) of the given parameter(s). #### Usage MultivariateNormal$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

deep

Whether to make a deep clone.