Title page for ETD etd-06272011-164137


Document Type Master's Dissertation
Author Loots, Mattheus Theodor
Email theo.loots@gmail.com
URN etd-06272011-164137
Document Title The development of the quaternion normal distribution
Degree MSc
Department Statistics
Supervisor
Advisor Name Title
Prof A Bekker Supervisor
Keywords
  • Wilks's statistic
  • quaternion Wishart distribution
  • real representation
  • characteristic function
  • quaternion matrix-variate beta type I distribution
  • Meijer's G-function
  • quaternion normal distribution
Date 2011-04-05
Availability unrestricted
Abstract
In 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.

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.

Please cite as follows:

Loots, MT 2011, The development of the quaternion normal distribution, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-06272011-164137/ >

E11/431/gm

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