Welch-Satterthwaite Approximation for t-Distribution Differences

Implements the Welch-Satterthwaite approximation for differences of non-standardized t-distributed random variables in both univariate and multivariate settings. The package provides methods for computing effective degrees of freedom and scale parameters, as well as distribution functions for the approximated difference distribution. The methodology extends the classical Welch-Satterthwaite framework from variance combinations to t-distribution differences through careful moment matching. Methods build on the classical Welch-Satterthwaite approach described in Welch (1947) and Satterthwaite (1946) .

wstdiff: Welch-Satterthwaite Approximation for t-Distribution Differences

Overview

The wstdiff package implements the Welch-Satterthwaite approximation for differences of non-standardized t-distributed random variables in both univariate and multivariate settings.

Installation

# Install from GitHub (once available)
# devtools::install_github("yourusername/wstdiff")

# Or install locally
devtools::install_local("path/to/wstdiff")

Usage

Univariate Case

library(wstdiff)

# Basic example
result <- ws_tdiff_univariate(
  mu1 = 0, sigma1 = 1, nu1 = 10,
  mu2 = 0, sigma2 = 1.5, nu2 = 15
)
print(result)

# Distribution functions
dtdiff(0, result)           # Density
ptdiff(0, result)           # CDF
qtdiff(c(0.025, 0.975), result)  # Quantiles
samples <- rtdiff(1000, result)  # Random generation

Multivariate Case (Independent Components)

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)
)

Multivariate Case (General Covariance)

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 <- ws_tdiff_multivariate_general(
  mu1 = c(0, 1), 
  Sigma1 = Sigma1, 
  nu1 = 10,
  mu2 = c(0, 0), 
  Sigma2 = Sigma2, 
  nu2 = 15
)

Reference

Yamaguchi, Y., Homma, G., Maruo, K., & Takeda, K. Welch-Satterthwaite Approximation for Difference of Non-Standardized t-Distributed Variables. (unpublished).

License

MIT License