In this paper we provide rather weak conditions on a distribution which would guarantee that the t-statistic of a random vector of order n follows the t-distribution with n-1 degrees of freedom. The results sharpen the earlier conclusions of Mauldon [Characterizing properties of statistical...

In this paper, we introduce center-similar multivariate distributions (CSDs) based on the vertical density representation theory. A number of families of CSDs are constructed and related statistical problems are briefly examined.