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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.

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