wstdiff (version 1.0.0)

ws_tdiff_multivariate_independent: Welch-Satterthwaite Approximation for Multivariate t-Differences (Independent)

Description

Approximates the distribution of differences between two independent p-dimensional vectors with independent t-distributed components.

Usage

ws_tdiff_multivariate_independent(mu1, sigma1, nu1, mu2, sigma2, nu2)

Value

An S3 object of class "ws_tdiff_multivariate_independent" containing:

mu_diff

Location vector of difference

sigma_star

Vector of effective scale parameters

nu_star

Vector of effective degrees of freedom

p

Dimension of the vectors

method

Character string "multivariate_independent"

Arguments

mu1

Location vector of first distribution (length p)

sigma1

Scale vector of first distribution (length p, all > 0)

nu1

Degrees of freedom vector of first distribution (length p, all > 4)

mu2

Location vector of second distribution (length p)

sigma2

Scale vector of second distribution (length p, all > 0)

nu2

Degrees of freedom vector of second distribution (length p, all > 4)

Details

This function applies the univariate Welch-Satterthwaite approximation component-wise when all components are mutually independent. Each component difference Zj = X1j - X2j is approximated independently using the univariate method.

This approach is optimal for:

• Marginal inference on specific components

• Cases where components have different tail behaviors

• Maintaining computational efficiency in high dimensions

See Also

ws_tdiff_multivariate_general for correlated components

Examples

result <- ws_tdiff_multivariate_independent(
  mu1 = c(0, 1), sigma1 = c(1, 1.5), nu1 = c(10, 12),
  mu2 = c(0, 0), sigma2 = c(1.2, 1), nu2 = c(15, 20)
)
print(result)