R/SDistribution_MultivariateNormal.R
MultivariateNormal.RdMathematical 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.
Returns an R6 object inheriting from class SDistribution.
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.
The distribution is supported on the Reals and only when the covariance matrix is positive-definite.
MultiNorm(mean = rep(0, 2), cov = c(1, 0, 0, 1))
cdf and quantile
are
omitted as no closed form analytic expression could be found, decorate with FunctionImputation for a numerical imputation.
N/A
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
distr6::Distribution -> distr6::SDistribution -> MultivariateNormal
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
propertiesReturns distribution properties, including skewness type and symmetry.
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$workingSupport()
new()Creates a new instance of this R6 class. Number of variables cannot be changed after construction.
MultivariateNormal$new(
mean = rep(0, 2),
cov = c(1, 0, 0, 1),
prec = NULL,
decorators = NULL
)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.
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.
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).
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.
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.
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.
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.
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.
getParameterValue()Returns the value of the supplied parameter.
idcharacter()
id of parameter support to return.
error(character(1))
If "warn" then returns a warning on error, otherwise breaks if "stop".
setParameterValue()Sets the value(s) of the given parameter(s).
MultivariateNormal$setParameterValue(
...,
lst = list(...),
error = "warn",
resolveConflicts = FALSE
)...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.