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Developments on MTP2 properties of absolute value multinormal variables with nonzero means

Developments on MTP2 properties of absolute value multinormal variables with nonzero means LetX=(X 1,...,X n )′ have a multivariate normal distribution with meanμ and covariance matrixΣ. In the caseμ=0, Karlin and Rinott[6] obtained a necessary and sufficient condition on Σ for |X|=(|X 1|,...|X n|)′ to be MTP2. In this paper we consider the caseμ≠0, and give some conditions under which |X| is MTP2. A necessary and sufficient condition is given for |X| to be TP2 whenn=2 andμ≠0. Some results about the TP2 stochastic ordering are also given. The results are applied to obtain positive dependence and associated inequalities for multinormal and related distributions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Developments on MTP2 properties of absolute value multinormal variables with nonzero means

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Publisher
Springer Journals
Copyright
Copyright © 1997 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02009546
Publisher site
See Article on Publisher Site

Abstract

LetX=(X 1,...,X n )′ have a multivariate normal distribution with meanμ and covariance matrixΣ. In the caseμ=0, Karlin and Rinott[6] obtained a necessary and sufficient condition on Σ for |X|=(|X 1|,...|X n|)′ to be MTP2. In this paper we consider the caseμ≠0, and give some conditions under which |X| is MTP2. A necessary and sufficient condition is given for |X| to be TP2 whenn=2 andμ≠0. Some results about the TP2 stochastic ordering are also given. The results are applied to obtain positive dependence and associated inequalities for multinormal and related distributions.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

References