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Singularities of Taylor’s power law in the analysis of aggregation measures

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  • De Bartolo, Samuele

Abstract

Taylor’s law is a well-known power law (TPL) for analysing the scaling behaviour of many fluctuating physical phenomena in nature. The scaling exponent b of this law forms the basis of the aggregation process to which a precise probability density function corresponds. In some phenomena, TPL behaviour with periodic components of the aggregates has been observed for small partitions, especially for physical processes characterised by values of b=1 where fluctuation-related aggregation processes are supported by Poissonian distributions. We intend to show that for values of b very close to unity it is possible to find a trend, in the double logarithmic scale, of the TPL that there are ‘periodic patterns’ (components) between variance and mean. This behaviour is found in other binomial-type distributions, of which the Poissonian is a particular case, with mappings characterised by a variance close to 1.

Suggested Citation

  • De Bartolo, Samuele, 2024. "Singularities of Taylor’s power law in the analysis of aggregation measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 654(C).
    • Handle: RePEc:eee:phsmap:v:654:y:2024:i:c:s0378437124006605
    DOI: 10.1016/j.physa.2024.130151
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