Moment-Matching Approximation for t-Distribution Differences

Implements the moment-matching approximation for differences of non-standardized t-distributed random variables in both univariate and multivariate settings. The package provides density, distribution function, quantile function, and random generation for the approximated distributions of t-differences. The methodology establishes the univariate approximated distributions through the systematic matching of the first, second, and fourth moments, and extends it to multivariate cases, considering both scenarios of independent components and the more general multivariate t-distributions with arbitrary dependence structures. Methods build on the classical moment-matching approximation method (e.g., Casella and Berger (2024) ).

mmtdiff: Moment-Matching Approximation for t-Distribution Differences

Overview

The mmtdiff package implements the moment-matching 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("yamagubed/mmtdiff")

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

Usage

Univariate Case

library(mmtdiff)

# Basic example
result <- mm_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 <- mm_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 <- mm_tdiff_multivariate_general(
  mu1 = c(0, 1), 
  Sigma1 = Sigma1, 
  nu1 = 10,
  mu2 = c(0, 0), 
  Sigma2 = Sigma2, 
  nu2 = 15
)