On the real representation of quaternion random variables

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Authors

Loots, Mattheus Theodor
Bekker, Andriette, 1958-
Arashi, Mohammad
Roux, Jacobus J.J.

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Publisher

Taylor & Francis

Abstract

For 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.

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Keywords

Characteristic function, Meijer’s G-function, Matrix-variate quaternion normal distribution, Quaternion Wishart distribution, Real representation, Wilks’ statistic

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Citation

Loots, 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.