  Shape dependence of higher order correlations introduces complication in
direct determination of these quantities. For this reason theoretical and
observational progress has been restricted in calculating one point
distribution functions and related moments. Methods based on factorial moments
of two point count probability distribution (cumulant correlators) were
recently shown to be efficient in subtracting discreteness effects and
extracting useful information from galaxy catalogs. We use these cumulant
correlators $Q_{NM}$ to study clustering in scale free simulations both in two
and three dimensions. Using this method in the highly nonlinear regime we were
able to separate hierarchal amplitudes $Q_3, R_a and R_b$ associated with
different tree graphs contributing to third and fourth order correlation
functions. They were found to increase with power on large scales. Results
based on factorial moments of one point cumulants show very good agreement with
that on cumulant correlators. Comparison of simulation results with
perturbation theory and extended perturbation theory were found to be in
reasonable agreement. Comparisons were also made against predictions from
hierarchal models for higher order correlations. We argue that finite volume
corrections are very important for computation of cumulant correlators.
