Abstract
A method has been proposed to process and analyze the proximity by type-defining characteristics of large aggregations M > 104 of various types Q > 102 of empirical discrete random frequency vectors RFV ≡ \(\nu ( \cdot ) = {{\nu }_{0}},~...~,{{\nu }_{l}}\) obtained from small volume samples \(10 \geqslant n = \sum\nolimits_{i = 1}^l {{{\nu }_{i}}(k = i)} \) of random counts k = 0, 1, …, l with mean value \(\bar {k} < 5\) over all samples. The method is based on a bijection between the RFV and its type-defining identifier \(I(\nu ,a) > 0\) a) > 0, which is a linear statistic in the form of the scalar product of ν and the non-RFV a. The discrete multimodal empirical distributions \(C\left( {I(\nu ,a)} \right)\) representing sequences of arranged by \(I(\nu ,a)\) and grouped peaks facilitate the analysis and prediction of the characteristics of peaks and the RFVs forming them with low frequencies of their occurrences at the given M value.
