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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 (unpublished).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

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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