The development of the quaternion normal distribution
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University of Pretoria
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.
Description
Dissertation (MSc)--University of Pretoria, 2010.
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, UCTD
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Loots, MT 2010, The development of the quaternion normal distribution, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/25903 >