  Given $0<q<1,$ every absolutely continuous distribution can be described in
two different ways: in terms of a probability density function and also in
terms of a $q$-density. Correspondingly, it has a sequence of moments and a
sequence of $q$-moments if those exist. In this article, new conditions on the
$q$-moment determinacy of probability distributions are derived. In addition,
results related to the comparison of the properties of probability
distributions with respect to the moment and $q$-moment determinacy are
presented.
