  A useful heuristic in the understanding of large random combinatorial
structures is the Arratia-Tavare principle, which describes an approximation to
the joint distribution of component-sizes using independent random variables.
The principle outlines conditions under which the total variation distance
between the true joint distribution and the approximation should be small, and
was successfully exploited by Pittel in the cases of integer partitions and set
partitions. We provide sufficient conditions for this principle to be true in a
general context, valid for certain discrete probability distributions which are
$\textit{perturbed log-concave}$, via a quantitative local central limit
theorem. We then use it to generalize some classical asymptotic statistics in
combinatorial theory, as well as assert some new ones.
