Statistical analysis based on quaternion normal random variables. (Afrikaans. English summary) Zbl 0586.62073
The quaternion normal distribution is derived and a number of characteristics are highlighted. The maximum likelihood estimation procedure in the quaternion case is examined and the conclusion is reached that the estimation procedure is simplified if the unknown parameters of the associated real probability density function are estimated. The quaternion estimator is then obtained by regarding these estimators as the components of the quaternion estimator. By means of an example attention is given to a test criterion which can be used in the quaternion model.
MSC:
62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
62H12 | Estimation in multivariate analysis |
62H15 | Hypothesis testing in multivariate analysis |
62H99 | Multivariate analysis |
15B33 | Matrices over special rings (quaternions, finite fields, etc.) |