  Motivated by the analysis of range queries in databases, we introduce the
computation of the Depth Distribution of a set $\mathcal{B}$ of axis aligned
boxes, whose computation generalizes that of the Klee's Measure and of the
Maximum Depth. In the worst case over instances of fixed input size $n$, we
describe an algorithm of complexity within $O({n^\frac{d+1}{2}\log n})$, using
space within $O({n\log n})$, mixing two techniques previously used to compute
the Klee's Measure. We refine this result and previous results on the Klee's
Measure and the Maximum Depth for various measures of difficulty of the input,
such as the profile of the input and the degeneracy of the intersection graph
formed by the boxes.
