Loots, Mattheus TheodorBekker, Andriette, 1958-Arashi, MohammadRoux, Jacobus J.J.2012-06-202013-06-302013Loots, MT, Bekker, A, Arashib, M & Roux, JJJ 2013, 'On the real representation of quaternion random variables', Statistics: A Journal of Theoretical and Applied Statistics, vol. 47, no. 6, pp. 1224-1240.0233-1888 (print)1029-4910 (online)10.1080/02331888.2012.695376http://hdl.handle.net/2263/19213For the first time, the matrix-variate quaternion normal and quaternion Wishart distributions are derived from first principles, i.e. from their real counterparts, exposing the relations between their respective densities and characteristic functions. Applications of this theory in hypothesis testing are presented, and the density function of Wilks’ statistic is derived for quaternion Wishart matrices.en© Taylor & Francis. This is an electronic version of an article published in Statistics: A Journal of Theoretical and Applied Statistics, vol. 47, no. 6, pp. 1224-1240, 2013, DOI:10.1080/02331888.2012.695376. Statistics: A Journal of Theoretical and Applied Statistics is available online at: http://tandfonline.com/loi/gsta20.Characteristic functionMeijer’s G-functionMatrix-variate quaternion normal distributionQuaternion Wishart distributionReal representationWilks’ statisticPostprint Article