  We propose to verify relations between quantities which characterize scaling
properties of high energy density fluctuations in terms of factorial moments
and newly introduced associated frequency moments. Typical examples are
presented in frame of systematics developed in the present paper. It involves
also several sorts of moments applied so far in the search for intermittency
and multifractality. Our approach takes the advantage of relations in which a
linear combination of associated frequency moments reduces statistical
fluctuations to the same extent as it is done by corresponding factorial
moments.
