Distributions of the compound and scale mixture of vector and spherical matrix variate elliptical distributions

Several matrix variate hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted hypergeometric type distributions with matrix arguments are then proposed. The scale mixture of left-spherical matrix variate elliptical distributions and univariate inverted hypergeometric type distributions is also derived as a particular case of the compound distribution approach.