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Computation of Multivariate Normal and t Probabilities

2009-07-09 Computers
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Release : 2009-07-09
Genre : Computers
Kind : eBook
Book Rating : 898/5 ( reviews)

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Book Synopsis Computation of Multivariate Normal and t Probabilities by : Alan Genz

Download or read book Computation of Multivariate Normal and t Probabilities written by Alan Genz. This book was released on 2009-07-09. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate normal and t 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.

Computation Of Multivariate Normal And T Probabilities

2009 Mathematical statistics
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Release : 2009
Genre : Mathematical statistics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Computation Of Multivariate Normal And T Probabilities by : P. Diggle P. Bickel (S. Fienberg, U. Gather)

Download or read book Computation Of Multivariate Normal And T Probabilities written by P. Diggle P. Bickel (S. Fienberg, U. Gather). This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt:

Monte Carlo Computation of Some Multivariate Normal Probabilities

1987
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Release : 1987
Genre :
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Book Synopsis Monte Carlo Computation of Some Multivariate Normal Probabilities by : STANFORD UNIV CA DEPT OF STATISTICS.

Download or read book Monte Carlo Computation of Some Multivariate Normal Probabilities written by STANFORD UNIV CA DEPT OF STATISTICS.. This book was released on 1987. Available in PDF, EPUB and Kindle. Book excerpt: The computation of orthant probabilities represents a difficult numerical problem for even modest dimensions. Moran (1984) proposed a Monte Carlo estimator of these quantities. In this paper a more general class of estimators is developed and methods for obtaining efficiency gains over Moran's procedure are discussed. Further, the authors discuss the Monte Carlo evaluation of the multivariate normal distribution function.

Computation of Multivariate Normal Probabilities Using Bivariate Conditioning with Simulation

2013
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Release : 2013
Genre :
Kind : eBook
Book Rating : 007/5 ( reviews)

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Book Synopsis Computation of Multivariate Normal Probabilities Using Bivariate Conditioning with Simulation by : Giang B. Trinh

Download or read book Computation of Multivariate Normal Probabilities Using Bivariate Conditioning with Simulation written by Giang B. Trinh. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt: We introduce algorithms for block LDLt decompositions of positive definite covariance matrices. These are extensions of the LDLt decomposition which requires D to be a diagonal matrix. We make use of these algorithms to represent the mutivariate normal (MVN) probability as a bivariate-iterated, trivariate-iterated and multivariate-iterated integrals. From there, we introduce a new method of approximating and simulating MVN probabilities using bivariate conditioning with simulation. Basic algorithms for bivariate, trivariate, multivariate conditioning are derived. A new approximate formula for multivariate normal probabilities which uses a product of bivariate normal probabilities is derived and considered with different variance reduction techniques. The new method is compared with approximation methods based on products of univariate normal probabilities. The new method uses conditioning with a sequence of truncated bivariate probabilities. Simulation methods which use Monte Carlo, and quasi-Monte Carlo point sets are developed.

Probability Integrals of Multivariate Normal and Multivariate T

1962 Multivariate analysis
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Release : 1962
Genre : Multivariate analysis
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Book Synopsis Probability Integrals of Multivariate Normal and Multivariate T by : S. S. Gupta

Download or read book Probability Integrals of Multivariate Normal and Multivariate T written by S. S. Gupta. This book was released on 1962. Available in PDF, EPUB and Kindle. Book excerpt: This paper gives a survey of the work on multivariate probability integral and related functions starting with the bivariate case and includes the author's recent work on the probability integrals of the multivariate normal and a multivariate analogue of Student's t. An annotated bibliography on evaluation of multivariate normal and t probability integrals (189 entries) is included. (Author).

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