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Computation of Multivariate Normal and t Probabilities

:	Alan Genz, Frank Bretz
:	Computation of Multivariate Normal and t Probabilities
:	Springer-Verlag
:	9783642016899
:	1
:	CHF 47.50
:

:	Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
:	English

:	126
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

Multivariate normal andt probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.

	Preface	5
	Contents	7
	1 Introduction	9
	1.1 A Historical Perspective	9
	1.2 Problem Setting	10
	1.3 Some Examples	12
	2 Special Cases	15
	2.1 Bivariate and Trivariate Probabilities	15
	2.2 Special Integration Regions	19
	2.3 Special Correlation Structures	24
	3 Methods That Approximate the Problem	29
	3.1 Boole s Formula Approximations and Bounds	29
	3.2 Correlation Matrix Approximations	32
	3.3 Other Approximations	33
	3.4 Asymptotic Expansions	34
	4 Methods That Approximate the Integral	36
	4.1 Reparameterizations	36
	4.2 Integration Methods	48
	5 Further Topics	62
	5.1 Linear Inequality Constraints	62
	5.2 Singular Distributions	63
	5.3 Related Integrals	66
	5.4 Numerical Tests	67
	5.5 Software Implementations	68
	5.6 Miscellaneous and Further References	75
	6 Applications	77
	6.1 Multiple Comparison Procedures	77
	6.2 Bayesian Statistics and Finance Applications	85
	A Description of the R Functions	96
	B Description of the MATLAB Functions	105
	References	109
	Index	127