Efficient multivariate-normal distribution calculations in Stata

The normal distribution holds significant importance in statistics. Much gathered real world data either is, or is assumed to be, normally distributed. Today though, a considerable amount of statistical analysis performed is not univariate, but multivariate in nature. Consequently, the multivariate normal distribution is of increasing importance. However, the complexity of this distribution makes computational analysis almost certainly necessary, and thus much research has been conducted in to developing efficient algorithms for its numerical analysis. Here we discuss our implementation of a certain choice of algorithm in Mata that allows its distribution function and equi-coordinate quantiles to be identified seamlessly for any choice of location vector and positive semi-definite covariance matrix. Moreover, we detail new commands to efficiently compute its density and to generate pseudo-random variables. We then discuss the performance of our commands relative to the presently available alternatives, and present how they provide greater generalisation and improved computational speed. Finally, through the example of designing a group sequential clinical trial, we demonstrate how our commands can be used easily to solve real-world problems facing Stata users.