Calculations involving the multivariate normal and multivariate t distributions with and without truncation

Area of Science:

• Statistics
• Computational Statistics

Background:

• The multivariate normal and noncentral multivariate t-distributions are fundamental in statistical modeling.
• Efficient computation of their distributional quantities is crucial for various applications.

Purpose of the Study:

• To present novel commands and Mata functions for evaluating distributional quantities.
• To enable efficient computation for both multivariate normal and noncentral multivariate t-distributions.

Main Methods:

• Development of specialized commands and Mata functions.
• Implementation of algorithms for calculating densities, distribution functions, equicoordinate quantiles, and pseudo-random vectors.
• Consideration of scenarios with and without variable truncation.

Main Results:

• Efficient computation of densities and distribution functions for specified distributions.
• Accurate generation of pseudo-random vectors.
• Capability to handle variable truncation in calculations.

Conclusions:

• The developed tools offer a robust and efficient solution for analyzing these complex distributions.
• These functions are valuable for researchers and practitioners in statistical analysis and simulation.