mvn: Generate Multivariate Normal Data \mathbf{X} \sim...
In jeksterslabds/jeksterslabRdata: Jekster's Lab Data Generation Utilities

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/mvn.R

Generates an n \times k multivariate data matrix or a list of n \times k multivariate data matrices of length R from the multivariate normal distribution

\mathbf{X} \sim \mathcal{N}_{k} ≤ft( \boldsymbol{μ}, \boldsymbol{Σ} \right) . %(\#eq:dist-X-mvn)

This function is a wrapper around MASS::mvrnorm().

mvn(
  n,
  mu = NULL,
  Sigma,
  tol = 1e-06,
  empirical = FALSE,
  df = FALSE,
  varnames = NULL,
  R = NULL,
  par = FALSE,
  ncores = NULL,
  mc = TRUE,
  lb = FALSE,
  cl_eval = FALSE,
  cl_export = FALSE,
  cl_expr,
  cl_vars
)

`n`	Integer. Sample size.
`mu`	Numeric vector. Location parameter mean vector \boldsymbol{μ} of length k.
`Sigma`	Numeric matrix. k \times k variance-covariance matrix \boldsymbol{Σ}.
`tol`	Numeric. Tolerance (relative to largest variance) for numerical lack of positive-definiteness in `Sigma`.
`empirical`	Logical. If `TRUE`, `mu` and `Sigma` specify the empirical, not population. mean and covariance matrix.
`df`	Logical. If `TRUE`, the function returns a data frame. If `FALSE`, the function returns a matrix.
`varnames`	Character string. Optional column names with the same length as `mu`.
`R`	Integer. Number of Monte Carlo replications. If `R` is not provided, the function produces a single random data set. If `R` is an integer greater than 1, (e.g., `R = 10`), the function produces multiple random data sets stored in each element of a list of length `R`. `par` and all succeeding arguments are only relevant when `R > 1`.
`par`	Logical. If `TRUE`, use multiple cores. If `FALSE`, use `lapply()`.
`ncores`	Integer. Number of cores to use if `par = TRUE`. If unspecified, defaults to `detectCores() - 1`.
`mc`	Logical. If `TRUE`, use `parallel::mclapply()`. If `FALSE`, use `parallel::parLapply()` or `parallel::parLapplyLB()`. Ignored if `par = FALSE`.
`lb`	Logical. If `TRUE` use `parallel::parLapplyLB()`. If `FALSE`, use `parallel::parLapply()`. Ignored if `par = FALSE` and `mc = TRUE`.
`cl_eval`	Logical. Execute `parallel::clusterEvalQ()` using `cl_expr`. Ignored if `mc = TRUE`.
`cl_export`	Logical. Execute `parallel::clusterExport()` using `cl_vars`. Ignored if `mc = TRUE`.
`cl_expr`	Expression. Expression passed to `parallel::clusterEvalQ()` Ignored if `mc = TRUE`.
`cl_vars`	Character vector. Names of objects to pass to `parallel::clusterExport()` Ignored if `mc = TRUE`.

The multivariate normal distribution has two parameters, namely the k \times 1 mean vector mu ≤ft( \boldsymbol{μ} \right) and the k \times k variance-covariance matrix Sigma ≤ft( \boldsymbol{Σ} \right). If mu is not provided, it is set to a vector of zeroes with the appropriate length.

Options for explicit parallelism are provided when R > 1 especially when R is large. See par and suceeding arguments.

If R = NULL or R = 1, returns an n \times k multivariate normal data matrix or data frame . If R is an integer greater than 1, (e.g., R = 10) returns a list of length R of n \times k multivariate normal data matrix or data frame.

Ivan Jacob Agaloos Pesigan

Venables, W. N., Ripley, B. D., & Venables, W. N. (2002). Modern applied statistics with S. New York, N.Y: Springer.

Wikipedia: Multivariate normal distribution

jeksterslabRdist::mvnpdf(), jeksterslabRdist::mvnll(), and jeksterslabRdist::mvn2ll(), for more information on the multivariate normal distribution.

Other multivariate data functions: mvnramsigma2(), mvnram()

mu <- c(100, 100, 100)
Sigma <- matrix(
  data = c(225, 112.50, 56.25, 112.5, 225, 112.5, 56.25, 112.50, 225),
  ncol = 3
)
X <- mvn(n = 100, mu = mu, Sigma = Sigma)
Xstar <- mvn(n = 100, mu = mu, Sigma = Sigma, R = 100)
str(Xstar, list.len = 6)