Are the marginals of the Multivariate t distribution with $\nu$ degrees of freedom univariate Student t distributions with $\nu$ degrees of freedom?



The proof is simple:

  1. The definition of a multivariate-t that you give is that it is a random variable that is the ratio of a multivariate Gaussian and the square-root of a Gamma variable
  2. The marginal distribution of that is the marginal distribution of the ratio of the Gaussian and the square-root of a gamma
  3. The distribution of a ratio of normal over square-root of Gamma is a univariate-t
| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.