Genz, A: Computation of Multivariate Normal Probabilities

Introduction.- Special Cases.- Methods That Approximate the Problem.- Methods That Approximate the Integral.- Further Topics: Linear Inequality Constraints.- Singular Distributions.- Singular Distributions.- Numerical Tests.- Software Implementations.- Applications.- Description of the R Functions.- Description of the MATLAB Functions.

From the reviews:"This book covers the computation of probabilities associated with the multivariate normal and multivariate t distributions. ... synthesizes many results published in statistics journals in recent years on this topic and provides a unique source of information on the computation of these probabilities, which arise very naturally for statistical inference in many modern applications. I believe that it fills a gap in the literature on multivariate statistics. ... this book will prove very useful to many statisticians in need of such probabilities for their applications." (Marc G. Genton, Journal of the American Statistical Association, Vol. 106 (496), December, 2011)"This monograph is a valuable source of information for people involved in the computations of multivariate normal and multivariate t probabilities. The material is assembled and presented in a consistent easy-flowing format. In general, this is an excellent monograph and a valuable addition to the personal library of people working in the areas of multivariate statistical analysis." (A. M. Mathai, Zentralblatt MATH, Vol. 1204, 2011)"This monograph is a valuable source of information for people involved in the computations of multivariate normal and multivariate t probabilities. The material is assembled and presented in a consistent easy-flowing format. In general, this is an excellent monograph and a valuable addition to the personal library of people working in the areas of multivariate statistical analysis." (A. M. Mathai, Zentralblatt MATH, Vol. 1204, 2011)