  A detailed understanding of all effects and influences on higher-order
correlations is essential. At low charged multiplicity, the effect of a
nonpoissonian multiplicity distribution can significantly distort correlations.
Evidently, the reference samples with respect to which correlations are
measured should yield a null result in the absence of correlations. We show how
the careful specification of desired properties necessarily leads to an
average-of-multinomials reference sample. The resulting internal cumulants and
their averaging over several multiplicities fulfil all requirements of
correctly taking into account nonpoissonian multiplicity distributions as well
as yielding a null result for uncorrelated fixed-N samples. Various correction
factors are shown to be approximations at best. Careful rederivation of
statistical variances and covariances within the frequentist approach yields
errors for cumulants that differ from those used so far. We finally briefly
discuss the implementation of the analysis through a multiple event buffer
algorithm.
