The Inverse Question of Elliptically Contoured Distribution

In this paper, we give a necessary and sufficient condition for the joint distribution of X₁ andX₂ to have elliptically contoured distribution, as X₁|X₂ =x₂ and X₂|X₁ =x₁ are elliptically contoured distributions. Same time, we had proved that the joint distribution of X₁ and X₂＝μ₂＋C'Y₂ to have elliptically contoured distribution, whenX₁|X₂ =x₂ and Y₂ are elliptically contoured distributions.