The development of the quaternion normal distribution

dc.contributor.advisorBekker, Andriette, 1958-en
dc.contributor.emailtheo.loots@gmail.comen
dc.contributor.postgraduateLoots, Mattheus Theodor
dc.date.accessioned2013-09-07T01:13:50Z
dc.date.available2011-06-28en
dc.date.available2013-09-07T01:13:50Z
dc.date.created2011-04-05en
dc.date.issued2010-12-28en
dc.date.submitted2011-06-27en
dc.descriptionDissertation (MSc)--University of Pretoria, 2010.en
dc.description.abstractIn this dissertation an overview on the real representation of quaternions in distribution theory is given. The density functions of the p-variate and matrix-variate quaternion normal distributions are derived from first principles, while that of the quaternion Wishart distribution is derived from the real associated Wishart distribution via the characteristic function. Applications of this theory in hypothesis testing is presented, and the density function of Wilks's statistic is derived for quaternion Wishart matrices.en
dc.description.availabilityunrestricteden
dc.description.departmentStatisticsen
dc.identifier.citationLoots, MT 2010, The development of the quaternion normal distribution, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/25903 >en
dc.identifier.otherE11/431/gmen
dc.identifier.upetdurlhttp://upetd.up.ac.za/thesis/available/etd-06272011-164137/en
dc.identifier.urihttp://hdl.handle.net/2263/25903
dc.language.isoen
dc.publisherUniversity of Pretoriaen_ZA
dc.rights© 2010, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.en
dc.subjectWilks's statisticen
dc.subjectQuaternion wishart distributionen
dc.subjectReal representationen
dc.subjectCharacteristic functionen
dc.subjectQuaternion matrix-variate beta type i distributionen
dc.subjectMeijer's g-functionen
dc.subjectQuaternion normal distributionen
dc.subjectUCTDen_US
dc.titleThe development of the quaternion normal distributionen
dc.typeDissertationen

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