  Operator regular variation reveals general power-law distribution tail decay
phenomena using operator scaling, that includes multivariate regular variation
with scalar scaling as a special case. In this paper, we show that a
multivariate Liouville distribution is operator regularly varying if its
driving function is univariate regularly varying. Our method focuses on
operator regular variation of multivariate densities, which implies, as we also
show in this paper, operator regular variation of the multivariate
distributions. This general result extends the general closure property of
multivariate regular variation established by de Haan and Resnick in 1987.
