mmtdiff (version 1.0.0)

mm_tdiff_multivariate_general: Moment-Matching Approximation for General Multivariate t-Differences

Description

Approximates the distribution of differences between two independent multivariate t-distributed random vectors with arbitrary covariance structure.

Usage

mm_tdiff_multivariate_general(mu1, Sigma1, nu1, mu2, Sigma2, nu2)

Value

An S3 object of class "mm_tdiff_multivariate_general" containing:

mu_diff

Location vector of difference

Sigma_star

Scale matrix

nu_star

Degrees of freedom (scalar)

method

Character string "multivariate_general"

Arguments

mu1

Location vector of first distribution (length p)

Sigma1

Scale matrix of first distribution (p x p, positive definite)

nu1

Degrees of freedom of first distribution (must be > 4)

mu2

Location vector of second distribution (length p)

Sigma2

Scale matrix of second distribution (p x p, positive definite)

nu2

Degrees of freedom of second distribution (must be > 4)

Details

This function handles the general case where components may be correlated within each multivariate t-distribution. The approximation uses a single scalar degrees of freedom parameter to capture the overall tail behavior.

Note: For high dimensions with heterogeneous component behaviors, consider using mm_tdiff_multivariate_independent instead.

Examples

Sigma1 <- matrix(c(1, 0.3, 0.3, 1), 2, 2)
Sigma2 <- matrix(c(1.5, 0.5, 0.5, 1.2), 2, 2)
result <- mm_tdiff_multivariate_general(
  mu1 = c(0, 1), Sigma1 = Sigma1, nu1 = 10,
  mu2 = c(0, 0), Sigma2 = Sigma2, nu2 = 15
)
print(result)