Scholary papers describing the methodology

The mvtnorm package implements methods to evaluate the probability, density, and quantile functions of the multivariate normal and t distributions. For the general case, tailored Monte Carlo methods described by Genz and Bretz (2009) are applied; for the bivariate normal the exact approach by Miwa, Hayter, and Kuriki (2003) is available as an alternative.

References

[1] T. Miwa, A. J. Hayter and S. Kuriki. “The Evaluation of General Non-centred Orthant Probabilities”. In: Journal of the Royal Statistical Society, Series B: Methodology 65 (2003), pp. 223–234. DOI: 10.1111/1467-9868.00382.

[2] A. Genz and F. Bretz. Computation of Multivariate Normal and t Probabilities. Vol. 195. Lecture Notes in Statistics. Heidelberg, Germany: Springer-Verlag, 2009.