Exponential scale mixture of matrix variate cauchy distribution

In this paper, we introduce a new subclass of matrix variate elliptically contoured distributions that are obtained as a scale mixture of matrix variate Cauchy distribution and exponential distribution. We investigate its properties, such as stochastic representation and characteristic function. Unlike Cauchy distribution, it is shown that the generating variate of the new distribution possesses finite moments. The distributions of the unbiased estimators of μ and Σ are derived. Furthermore, an identity involving a special function with a matrix argument is also obtained.