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Motivated by a real data analysis,we in this paper propose a new multivariate t(MVT)distribution by allowing variable degrees of freedom for each univariate component.This new distribution is called Type Ⅱ MVT distribution,which possesses several remarkable features including(1)all components follow univariate t-distributions with possible different degrees of freedom,(2)it could include components following the multivariate normal distributions when the corresponding degrees of freedom approach to infinity,and(3)it contains the product of independent t-distributions as a particular case.