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Generate Multivariate Normal Random Vector

Source: R/generate-process.R
sim_mnormal.Rd

This function samples n x muti-dimensional normal random matrix.

Usage

sim_mnormal(
  num_sim,
  mu = rep(0, 5),
  sig = diag(5),
  method = c("eigen", "chol")
)

Arguments

num_sim

Number to generate process

mu

Mean vector

sig

Variance matrix

method

Method to compute \(\Sigma^{1/2}\). Choose between eigen (spectral decomposition) and chol (cholesky decomposition). By default, eigen.

Value

T x k matrix

Details

Consider \(x_1, \ldots, x_n \sim N_m (\mu, \Sigma)\).

  1. Lower triangular Cholesky decomposition: \(\Sigma = L L^T\)

  2. Standard normal generation: \(Z_{i1}, Z_{in} \stackrel{iid}{\sim} N(0, 1)\)

  3. \(Z_i = (Z_{i1}, \ldots, Z_{in})^T\)

  4. \(X_i = L Z_i + \mu\)