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Article: Uniform distributions in a class of convex polyhedrons with applications to drug combination studies

TitleUniform distributions in a class of convex polyhedrons with applications to drug combination studies
Authors
KeywordsConvex polyhedron
Drug combination study
Stochastic representation
Tetragon
Uniform design
Uniform distribution
Issue Date2009
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmva
Citation
Journal Of Multivariate Analysis, 2009, v. 100 n. 8, p. 1854-1865 How to Cite?
AbstractMotivated by experimental designs for drug combination studies, in this paper, we propose a novel approach for generating a uniform distribution on an arbitrary tetragon in two-dimensional Euclidean space R 2. The key idea is to construct a one-to-one transformation between an arbitrary tetragon and the unit square [0, 1] 2. This transformation then provides a stochastic representation (SR) for the random vector uniformly distributed on the tetragon. An algorithm is proposed for generating a uniform distribution in an arbitrary triangular prism in R 3. In addition, we develop methods for generating uniform distributions in a class of convex polyhedrons in n-dimensional Euclidean space R n. In particular, SRs for uniform distributions in regions with order restrictions are presented. We apply the proposed method to the experimental design for a drug combination study. © 2009 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/82750
ISSN
2015 Impact Factor: 0.857
2015 SCImago Journal Rankings: 1.458
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTian, GLen_HK
dc.contributor.authorFang, HBen_HK
dc.contributor.authorTan, Men_HK
dc.contributor.authorQin, Hen_HK
dc.contributor.authorTang, MLen_HK
dc.date.accessioned2010-09-06T08:32:59Z-
dc.date.available2010-09-06T08:32:59Z-
dc.date.issued2009en_HK
dc.identifier.citationJournal Of Multivariate Analysis, 2009, v. 100 n. 8, p. 1854-1865en_HK
dc.identifier.issn0047-259Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/82750-
dc.description.abstractMotivated by experimental designs for drug combination studies, in this paper, we propose a novel approach for generating a uniform distribution on an arbitrary tetragon in two-dimensional Euclidean space R 2. The key idea is to construct a one-to-one transformation between an arbitrary tetragon and the unit square [0, 1] 2. This transformation then provides a stochastic representation (SR) for the random vector uniformly distributed on the tetragon. An algorithm is proposed for generating a uniform distribution in an arbitrary triangular prism in R 3. In addition, we develop methods for generating uniform distributions in a class of convex polyhedrons in n-dimensional Euclidean space R n. In particular, SRs for uniform distributions in regions with order restrictions are presented. We apply the proposed method to the experimental design for a drug combination study. © 2009 Elsevier Inc. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmvaen_HK
dc.relation.ispartofJournal of Multivariate Analysisen_HK
dc.subjectConvex polyhedronen_HK
dc.subjectDrug combination studyen_HK
dc.subjectStochastic representationen_HK
dc.subjectTetragonen_HK
dc.subjectUniform designen_HK
dc.subjectUniform distributionen_HK
dc.titleUniform distributions in a class of convex polyhedrons with applications to drug combination studiesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0047-259X&volume= 100&issue=8&spage=1854&epage=1865&date=2009&atitle=Uniform+Distributions+in+a+Class+of+Convex+Polyhedrons+with+Applications+to+Drug+Combination+Studiesen_HK
dc.identifier.emailTian, GL: gltian@hku.hken_HK
dc.identifier.authorityTian, GL=rp00789en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jmva.2009.02.011en_HK
dc.identifier.scopuseid_2-s2.0-67349268970en_HK
dc.identifier.hkuros163564en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-67349268970&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume100en_HK
dc.identifier.issue8en_HK
dc.identifier.spage1854en_HK
dc.identifier.epage1865en_HK
dc.identifier.isiWOS:000266565200022-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridTian, GL=25621549400en_HK
dc.identifier.scopusauthoridFang, HB=7402543028en_HK
dc.identifier.scopusauthoridTan, M=7401464681en_HK
dc.identifier.scopusauthoridQin, H=35091584500en_HK
dc.identifier.scopusauthoridTang, ML=7401974011en_HK
dc.identifier.citeulike5024029-

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