Generalized Gaussian Distribution with Augmented Pure Quaternion Random Variable

Quaternion random signals can be analyzed using augmented second-order statistics. If these signals are treated as the augmented quaternion valued random variables, then they can be modeled with the quaternion generalized Gaussian probability density function. In the case of pure quaternions, this probability density function becomes a limiting case. Therefore, for this case, this article introduces the dedicated generalized Gaussian distribution of an augmented quaternion random variable for pure quaternions.